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Sylow theory for groups of finite Morley rank. (English. Russian original) Zbl 0729.20012
Sib. Math. J. 30, No. 6, 873-877 (1989); translation from Sib. Mat. Zh. 30, No. 6(178), 52-57 (1989).
The aim of this paper is to show how using an axiomatic approach to \(\omega\)-stable groups of finite Morley rank we can get some analogy with finite group theory. Notions and results connected to the notion of Sylow 2-subgroups in these groups are discussed. The following analog of the Baer-Suzuki theorem is proved: Thm. Let G be an \(\omega\)-stable finite Morley rank group, K a class of conjugate elements of G. If \(<x,y>\) is a 2-group for all x,y in K then the normal subgroup \(<K>\trianglelefteq G\), generated by K is almost nilpotent.

MSC:
20E07 Subgroup theorems; subgroup growth
20A15 Applications of logic to group theory
03C60 Model-theoretic algebra
03C45 Classification theory, stability, and related concepts in model theory
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