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

2014/09/27 by E. I. Khukhro, N. Yu. Makarenko, Khukhro, E. I. +4
Computer Science · Mathematics · #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1409.7807

minor corrections and additions

openalex publication_date 2014/09/27 · arxiv created 2015/04/16 · arxiv updated 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that a finite group G admits an automorphism φ of order 2ⁿ such that the fixed-point subgroup C_G(φ^2^n-1) of the involution φ^2^n-1 is nilpotent of class c. Let m=|C_G(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.

Citations

• Large and symmetric: The Khukhro–Makarenko theorem on laws — without laws

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