Finite groups and Lie rings with an automorphism of order 2n

Khukhro, E. I. and Makarenko, N. Yu. and Shumyatsky, P. (2017) Finite groups and Lie rings with an automorphism of order 2n. Proceedings of the Edinburgh Mathematical Society, 60 (2). pp. 319-412. ISSN 0013-0915

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Abstract

Abstract. Suppose that a finite group G admits an automorphism ϕ of order 2n such that the fixed-point subgroup CG (ϕ2n−1) of the involution ϕ2n−1 is nilpotent of class c. Let m = |CG (ϕ)| be the number of fixed points of ϕ. It is proved that G has a characteristic soluble subgroup of derived length bounded in terms of n, c whose index is bounded in terms of m, n, c. A similar result is also proved for Lie rings.

Keywords:Automorphism, Finite groups, Lie rings, bmjgoldcheck
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:17243
Deposited On:22 Apr 2015 10:40

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