A propos e'equations generiques

Journal of Symbolic Logic 57 (2):548-554 (1992)

We prove that a stable solvable group $G$ which satisfies $x^n = 1$ generically is of finite exponent dividing some power of $n$. Furthermore, $G$ is nilpotent-by-finite. A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian)
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DOI 10.2307/2275290
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Commutator Conditions and Splitting Automorphisms for Stable Groups.Frank O. Wagner - 1993 - Archive for Mathematical Logic 32 (3):223-228.

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