The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. Unfortunately in (...) the last section of the latter paper there is an irrepairable mistake. Here we give a new proof of the Schur-Zassenhaus Theorem using the results of [2] up to the last section and a new result that we are going to state below.The second author has shown in [11] that a nilpotentω-stable group is the central product of a divisible subgroup and a subgroup of bounded exponent, generalizing a well-known result of Angus Macintyre about abelian groups [8]. One could ask a similar question for solvable groups: are they a product of two subgroups, one divisible, one of bounded exponent? One is allowed to be hopeful because of the well-known decomposition of the connected solvable algebraic groups over algebraically closed fields as the product of the unipotent radical and a torus. (shrink)

In the past twenty years, all the key authors who wrote about the state of postmodernity either began to be engaged in other research areas (Fredric Jameson) or declared that the postmodernism is dead (Linda Hutcheon). Since 2000, when the fatigue from the postmodernism became evident to everyone, various researchers, critics and theorists began to offer their concepts of our era. However, all these theories, emphasizing the change of cultural paradigms, interpret culture traditionally not paying attention to total digitalization and (...) the introduction of new technologies into our lives. However, in two concepts of our time these processes become central. These are the concepts of the digimodern and automodern. The focus of this article is the idea of automodernism, proposed by the American social theorist Robert Samuels in 2007/2009. He believes that our world is characterized by two contradictory tendencies – automation and the desire for autonomy (personal freedom). From his point of view, the former often does not allow to reach the latter due to certain circumstances. Samuels, using the example of a car, a personal computer, the Internet, etc., shows what exactly our culture is in the broadest sense. Analyzing the concept of “digital youth,” he also pays attention to the formation of a new subjectivity of the era of automodernity. Finally, the most interesting part of the concept of automodernism, which is most relevant today, is the criticism of leftwing social and philosophical concepts (Slavoj Žižek, Jameson) and cultural theories (Henry Jenkins). At the end of the article, the author mentions Adam Greenfield’s latest book Radical Technologies: The Design of Everyday Life. Thanks to this book, Samuels’ theory can be verified. (shrink)

The latest book by Russian philosopher Sergey Mareev consists of two parts: recollections of his teacher Evald Ilyenkov, and reflections on some of the key themes of Ilyenkov’s philosophical heritage. The author traces several polemical lines related to the problem of the ideal, dialectics of the abstract and the concrete, the principle of historicism, as well as Ilyenkov’s interpretation of Spinoza and Hegel.

The concept of sustainable development considers environmental, social and economic issues in general. And the goals of resource conservation and socio-economic development do not contradict each other, but contribute to mutual reinforcement. The purpose of this study is to build and test an economic and mathematical model for the formation of strategies for the behavior of an economic entity with an increase in the impact of negative environmental factors. The proposed strategies and their models are based on the income-expenditure balance (...) equation, which takes into account both quantitative and qualitative characteristics. The constructed models are considered in the state space. The research methodology is based on building models in the form of linear combinations of functions of a homogeneous external impact and various spatial combinations of economic sources (sinks). The study makes it possible to assess the dependence of the amount of resources used for life support on the chosen adaptive strategy. Within the framework of the proposed model, it was found that the criterion for the effectiveness of the applied strategy can be an indicator of satisfaction with the state, the preservation of which, simultaneously with the preservation of the size of resources used, corresponds to the direction of optimization. This approach is consistent with the concept of sustainable development. (shrink)

The article discusses an actual problem of the contemporary social theory – a problem of post-postmodernism that is the answer to the question: what comes to replace the supposedly outdated postmodernism. Post-postmodernism in an umbrella term that brings together various concepts like digimodernism, automodernism, metamodernism, hypermodernism, supermodernism, etc. One of the replacing postmodernism theories is the French curator and art theorist Nicolas Bourriaud’s concept that was called “altermodern” or “other modernism.” In his previous books Bourriaud proposed to rewrite modernism and, (...) as the result, developed a new theory. The concept appeared in 2009 when Bourriaud presented the exhibition in London, timed to the publication of his manifesto Altermodern, and edited and published the book of collected papers of the same title. Globalization, which opened borders for art, is a central concept of the altermodernism theory. The main terms of altermodern are heterochrony (time diversity) and viatorisation (nomadism). The main social subject of the alternodern era is a free travelling artist, who interprets the meanings of “rewritten” art for the public. They are “rewritten” because Bourriaud proposes to use phenomena and products of past ages to make them work in a new way. However Bourriaud’s concept should be considered critically, as it was formerly done by several researchers. The article proposes a critical review that answers to the question: to what extent the idea of altermodern is heuristic and therefore it could compete with other concepts that abolish postmodern. The author gives a negative answer to this question first of all because altermodern just borrows a lot of elements of the language and apparatus of postmodernism and actually does not offer anything new. (shrink)

Introduction. A radical tendency in modern approaches to understanding the mechanisms of the brain is the tendency of some scientists to believe that the brain is a receptor capable of capturing thoughts; the nature of the occurrence of the thoughts themselves, however, is not to be clarified. However, speech expressing thoughts is undoubtedly the result of the work of the brain, so studies of the frequency structure of speech can be the basis for considering the material structure of the brain (...) as a kind of “antenna”. In this approach, the problem of noise protection against the background of the undeniable frequency similarity of speech and music appears to us from somewhat different positions. This study raises the question of how essential the overall height of the musical system is to the perception of music (are there musical systems that are harmful or useful, in terms of their effects on the psyche). This question is also relevant to speech perception.Methodology and sources. The main sources in which the work of the brain and the essence of consciousness are considered from the positions indicated above were for us the work of American and British neurophysiologists and psychiatrists (Sam Parnia, Peter Fenwick). These scientists are studying the phenomena that accompany clinical death, and argue that at these moments the brain functions to the greatest extent as a receiving “antenna”. Assuming that any antenna is to be tuned, we are trying to identify possible ways to “tune” the brain. To do this, we propose to study the frequency characteristics of speech (in the simplest case, when singing vowels in a calm state) for their belonging to a particular musical system, as well as the peculiarities of music perception depending on the musical system (on the height of the note “la”). Varying the frequency characteristics of speech in a particular musical system can be considered, in our opinion, the main way to “tune” the brain. The methodology of the method is based on the use of frequency analysis of sound and the basic provisions of the elementary theory of music.Results and discussion. The main conclusion made by Western psychiatrists is the brain is not an organ of thought, consciousness exists independently from outside, the work of consciousness cannot be explained by the functioning of the brain – it requires a hardware check. If the neural network is an “antenna” that captures thoughts, and its “adjustment” at the physical level can be carried out (and is carried out) through sensory systems (including the hearing organ), the study of the frequency structure of speech will answer a number of important questions, including including related and higher brain functions (insight, creativity). Our experiments (Saint Petersburg Electrotechnical University, FIBS, department of EUT) showed that the influence of the “increased” or “lowered” musical-speech system on brain activity is insignificant. The study revealed the equiprobability of the frequency structure of speech. Since our brain lacks some characteristic set of frequencies – elements of a uniformly temperamental system, it is not necessary to talk about the harmful (or any other noise) effect of the “raised” and “lowered” systems due to deviation from the “internal standard”.Conclusion. In response to the assumptions made by Western experts, we proposed a frequency interpretation of the processes occurring in the brain, which, perhaps, will explain in more detail such phenomena as inspiration, discovery, etc., which occur with minimal activity of consciousness. Despite the limited methods of hardware study of factors that influence the activity of the brain and largely determine its higher functions (for example, creativity), the results of the brain's work in relation to music (both in terms of its creation and in terms of our reaction to it) are quite analyzable, which was shown in this study. The “musicality” of speech is extremely vividly represented in its frequency structure and allows one to reveal, to one degree or another, the features of the brain. (shrink)

The article considers the problem of universal basic income. The author believes that this topic can become one of the most relevant for social-philosophical research. The author notes that although the problem has been of concern to philosophers and scientists for a long time, it has become especially relevant only recently – over the past ten years. The following reasons are given as an explanation: recent experiments on the introduction of a universal basic income in Western countries, the trend toward (...) automation and technologization, the transformation of the economy, which is becoming more and more precarious. The author notes that the topic of universal basic income has become relevant even in Russian science, however, not in social philosophy, as in the West, but mainly in economics. The author argues that, since the discussion about basic income in the economic dimension has already taken place, it should be expanded to the field of social philosophy. To do this, the author raises a number of questions that will shed light on the social-philosophical nature of the problem of universal basic income – freedom, justice, welfare state, etc. Special attention is paid to the curious ideological transformations that became possible by the emergence of topic of basic income. First of all, basic income contributes to the formation of new ideologies, such as post-capitalism. Secondly, basic income itself can be considered as a new ideology, which is a synthesis of other ideological trends – libertarianism, feminism, Marxism, etc. Thirdly, post-capitalism, which emphasizes basic income, opens up much more significant problems than replacing labor and turning all people into a precariat. The author hopes that this paper will serve as the beginning of the discussion of the issue of basic income in the context of social-philosophical knowledge. (shrink)

The latest book by Russian philosopher Sergey Mareev consists of two parts: recollections of his teacher Evald Ilyenkov, and reflections on some of the key themes of Ilyenkov’s philosophical heritage. The author traces several polemical lines related to the problem of the ideal, dialectics of the abstract and the concrete, the principle of historicism, as well as Ilyenkov’s interpretation of Spinoza and Hegel.

The two volumes of letters by Mikhail Lifschitz, recently published in Russian, reveal for the first time certain aspects of his relationship with György Lukács and his general intellectual and cultural role in the long history of Soviet aesthetics. The first volume contains all the known letters between Lifschitz and Lukács; the second volume contains the letters from Lifschitz to three of his younger colleagues. Both volumes throw considerable light on the development of Marxist aesthetics in the Soviet Union from (...) the 1930s to the 1980s. The extensive commentaries and notes provide context for the various discussions in the letters and situate the main issues under consideration within the wider historical and social context of the period. (shrink)

O objetivo deste artigo é propor, de modo simples e saudável, uma releitura transformadora na relação entre os ministérios ordenados e a missão leiga, sobretudo no tocante à espiritualidade laical como colaboração eclesial. Com efeito, desde o tempo de Jesus, o protagonismo leigo, como cooperador à evangelização sempre foi ressaltado e muito bem aproveitado pelo Mestre; dessa forma, nota-se o quanto a Igreja carece hoje dessa ajuda primordial. Não por menos, o Concilio Vaticano II, no decreto Apostolicam Actuositatem, diz que (...) o fiel leigo é indispensável á missão da Igreja. Assim, entre tantas orientações, o mesmo decreto convoca a renovar e valorizar o ardor missionário com o apostolado leigo no interior da Igreja. Nesse sentido, é urgente a aplicação do pedido solicitado no Concílio Vaticano II para os tempos atuais, visando à sua concretização e não ficar somente em uma longínqua teoria. É nesta óptica, que a V CELAM, realizada em Aparecida, enfatiza mais uma vez a indispensabilidade do leigo como colaborador profícuo na missão eclesial. Por fim, vemos em muito a realização exemplar de muitos fiéis leigos batizados em seu exercício de ministros não-ordenados que oferecem subsídios riquíssimos para santificar a vida na Igreja. (shrink)

t. 1. Filosofski sŭchinenii︠a︡, 1933-1937 ; Obshta teorii︠a︡ na izkustvoto -- t. 2. Teorii︠a︡ na otrazhenieto. 5. izd. -- t. 3. Izbrani filosofski sŭchinenii︠a︡, 1961-1976.

t. 1. Otrazhenie, poznanie, tvorchestvo.

TOPOGRAPHICAL MISSIONS ΤΟ LATO I (2005-2007): A CRITICAL ANALYSIS OF THE PLAN BY J. DEMARGNE AND V. SEYK (1901) In the years 2005 and 2007 the site of Lato in Crete was the object of three new topographical and geomorphological study campaigns. The works carried out over the entire site permitted in particular the analysis of the only to date available complete plan of the city, that of J. Demargne and the architect V. Seyk undertaken in 1900. The objectif was (...) to establish its documentary interest and limits in use, and thus better prepare new measurements and guide renewed field work. To do this, it was first necessary (I) to retrace the history of previous graphic documentation, (II) to analyse the work of J. Demargne and V. Seyk, so as (III) to gauge its value against the standards of current research, and (IV) to establish its interest in terms of the cultural resource management of the site. A second paper to appear in BCH will develop, on basis of a new documentation, the urban and morphological analysis of the remains of Lato. (shrink)

COSTA, Alexandre da. Fundamentos da bioética: estudo sobre o pensamento de Hugo Tristram Engelhardt Jr. FERREIRA, Amauri Carlos. O imaginário religioso e modos de vida urbana: experiência e memória da Juventude Católica em Belo Horizonte – MG, anos 80. GONÇALVES, Davidson Sepini. O Panóptico de Jeremy Bentham: por uma leitura utilitarista. GÓIS, Aurino José. Parque Municipal de Belo Horizonte: público, apropriações e significados. FARIA, Paulo Antônio Couto. Teologia no limiar da filosofia: a modernidade e o encontro fé e razão na (...) obra de Henrique Cláudio de Lima Vaz. (shrink)

La polémique entre V. Soloviev et L. Lopatine met en lumière les recherches de la philosophie russe sur son mode propre de compréhension du Moi. Pour Soloviev, on ne peut attribuer au sujet de la conscience en tant que tel une réalité autre que phénoménologique. Lopatine propose une variante, proche de Leibniz, selon laquelle le Moi est une conscience subjective, présente aux différents niveaux du développement spirituel. Cette interprétation est reprise et développée, dans une certaine mesure, par N. Losski. G. (...) Chpet tire un bilan de la discussion, en posant le caractère « communautaire » [ obščnost ’] particulier du Moi, qui se réalise non par la « généralisation » [ obobščenie ] mais par la « communication » [ obščenie ]. (shrink)

The article devotes to the initial stage of I.S. Turgenev’s creativity path, when he intended to devote himself to philosophy. The first part of the historical and philosophical research covers the studentship stage of his life, Turgenev’s involvement to the University course of philosophy primarily in Moscow, then in St. Petersburg universities. Everything happened at Moscow University due to Professor M.G. Pavlov, Shelling’s philosophy follower, who was teaching physics in a philosophical format. He listened course of lectures on metaphysics (...) at St.-Petersburg University, given by A. A. Fisher, who was one of the first who started to teach philosophy in accordance with Uvarov’s ideological triade “Orthodoxy, Autocracy and Nationality”. The second part touches upon the period of education abroad. After he had finished the philological faculty of St.-Petersburg University in 1837, he became convinced that Russian universities could provide only preliminary education and real source of knowledge could be found only abroad; that is why he goes “to finish his education” in Berlin. There he studied ancient languages, history and Hegel’s philosophy under the guidance of Professor Werder. Turgenev also prepared different parts of Shelling’s teaching for publishing in Russian periodic, after famous philosopher had given lectures in University of Berlin. The last part of this article gives a picture of Turgenev attempts to receive masters’ degree and tries to take place at the Department of Philosophy. At the beginning of 1842, after presenting the diploma of candidate, granted by St.-Petersburg University, he asked Moscow University Council to give him a permission to receive the masters’ degree; his utter motive was to occupy the place at the Department of Philosophy, which was vacant for a long time. But he failed to do so in Moscow and moved to St.-Petersburg, where he tried to pass exams needed to get degree again. However, he failed again due to not giving the dissertation work; as the result, he didn’t receive masters’ degree and, furthermore, he dedicated himself entirely to literature. However, Turgenev saved his interest to philosophical problems, which he tried to solve in prose format. (shrink)

The article introduces Ilyenkov as an original psychologist, who, based on his Marxist reading of Spinoza, provides a novel solution to the psychophysical problem. Rejecting Pavlov's stimulus-reaction theory, he argues for the unifying concept of "thinking body," which allows him to explain thinking as a mode of the corporeal action in accordance with the universal forms of the world of objects. This understanding transforms psychology from purely magic discipline into scientific theory, which has a solid practical foundation.

This is a long-awaited reprint of the major work of the late Alexandre Koyré, one of the greatest masterpieces of the history of Western philosophy. The early nineteenth century saw a revival of Boehme studies but even the commentaries of Franz von Baader could not be substituted for a scholarly synthesis of Boehme's thought. Boehme is a universe of his own, and only the immense learning of a man like Koyré, with his rare ability to synthesize and clarify, could have (...) done justice to him. Through and beyond the rich and baroque splendor of the cosmic poetry of the Dawn of the Mysterium Magnum, we see the birth of the modern philosophical spirit. What Boehme offers us is a philosophy of freedom, and, despite the modesty of his comparisons, Koyré does not fail to show how all this anticipates the greatest Idealistic systems.--M. J. V. (shrink)

This article considers the issues of adaptation and organization of the educational process, barrier-free environment and readiness for professional activity of students with disabilities in inclusive education in conditions of inclusive education in a medical university. The relevance of this work is determined by one of the priority areas of state policy in the field of higher education – access to higher education for people with disabilities in inclusive education. Inclusive education at the university is designed to ensure not only (...) the realization of the right of students with disabilities in inclusive education to higher education, but also to solve the problems of socialization and professional demand for such people. In order to improve the process of introducing inclusive education at the Ryazan State Medical University named after Academician I.P. Pavlov, a study was conducted, the main problems and ways of solving them were identified, related to the organization of the educational process, the conditions of the barrier-free environment and the readiness for professional activity of students with disabilities in inclusive education. An increase in the proportion of university teachers who have undergone advanced training in inclusive education also contributes to solving problems. Adaptation of educational programs and educational and methodological support for persons with disabilities includes psychological, pedagogical and tutor support etc. The organization of the educational process using distance education technologies is one of the priority conditions for teaching students with disabilities and/or HIA. The use of this technology makes it possible to significant-ly expand and modify some educational standards for students with disabilities in inclusive education, namely, to create an individual way for each student with disabilities in inclusive education in a medical university. It is proposed to use training techniques such as: online consultation of teachers; VR technologies; availability of training materials 24/7; online webinars that facilitate the inclusion of such students in the educational and research activities of the university. The professionally organized educational space and educational process of the university provide not only a high level of mastery of professional competencies, but also contribute to the formation of personal qualities of students with disabilities in inclusive education, necessary for their successful socialization, life and activity in society. (shrink)

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

Обґрунтовано стратегію високочастотної біржової торгівлі (high-frequency trading) акціями. Для цього досліджено особливості та обмеження біржової високочастотної торгівлі, визначено верхню межу прибутку агресивного «шкідливого» високочастотного трейдера, обґрунтовано оптимальну частоту стратегії біржової високочастотної торгівлі акціями, розглянуто емпіричне підтвердження прогнозованості біржових курсів акцій на надкоротких горизонтах інвестування.

Natural modalities are often analysed from an abstract point of view where they are associated with putative laws of nature. However, the way possibilities are represented in physics is more complex. Lagrangian mechanics, for instance, involves two different layers of modalities: kinematical and dynamical possibilities. This paper examines the status of these two layers, both in the classical and quantum case. The quantum case is particularly problematic: we identify four possible interpretive options. The upshot is that a close inspection of (...) the way possibilities are represented in physics could lead to new ways of thinking about natural modalities. (shrink)