Abstract.
Given a simple non-trivial finite-dimensional Lie algebra L, fields \(K_i\) and Chevalley groups \(L(K_i)\), we first prove that \(\Pi_{\mathcal{U}} L(K_i)\) is isomorphic to \(L(\Pi_{\mathcal{U}}K_i)\). Then we consider the case of Chevalley groups of twisted type \({}^n\!L\). We obtain a result analogous to the previous one. Given perfect fields \(K_i\) having the property that any element is either a square or the opposite of a square and Chevalley groups \({}^n\!L(K_i)\), then \(\pu{}^n\!L(K_i)\) is isomorphic to \({}^n\!L(\pu K_i)\). We apply our results to prove the decidability of the set of sentences true in almost all finite groups of the form L(K) where K is a finite field and L a fixed untwisted Chevalley type.
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Received: 19 November 1993 / Revised version: 15 November 1995
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Point, F. Ultraproducts and Chevalley groups. Arch Math Logic 38, 355–372 (1999). https://doi.org/10.1007/s001530050131
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DOI: https://doi.org/10.1007/s001530050131