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Post-classification version of Jordan’s theorem on finite linear groups. (English) Zbl 0542.20026
The author gives some results on the orders of finite subgroups $$H$$ of $$GL(n,K)$$, $$K$$ a field. If $$K={\mathbb{C}}$$, the author provides an upper bound for $$|H:A|$$ where $$A$$ is an abelian normal subgroup of $$H$$. This improves a classical result of Jordan. If $$char K=p(\neq 0)$$ there is a normal subgroup $$N$$ such that $$N/O_ p(H)$$ is the direct product of an abelian $$p'$$-group with the central product of groups of Lie type of characteristic $$p$$. Here the author gives an upper bound for $$|H:N|$$ and thus improves a result of R. Brauer and W. Feit [Ann. Math., II. Ser. 84, 119-131 (1966; Zbl 0142.26203)]. In the proofs the classification of finite simple groups is used.
Reviewer: U.Dempwolff

##### MSC:
 20G15 Linear algebraic groups over arbitrary fields 20E07 Subgroup theorems; subgroup growth 20D05 Finite simple groups and their classification
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