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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

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