Nilpotent periodic groups with an almost regular automorphism of prime order
type: Item
instance of: scholarly article
title: Nilpotent periodic groups with an almost regular automorphism of prime order
zbMATH Open document ID: 0663.20039
DOI: 10.1007/BF01980244
published in: Algebra and Logic
publication date: 1987-01-01T00:00:00Z
review text: It is proved that there exist two natural-valued functions f(p,n), g(p,n) for p prime and n natural arguments such that every nilpotent periodic group G having an automorphism of prime order p with precisely n fixed points contains a subgroup H such that the nilpotency class of H is not greater than f(p,n) and \(| G:H| \leq g(p,n)\) (Theorem 1). As a corollary of this result, a locally soluble periodic group G containing an element of prime order with \(| C_ G(a)| <\infty\) is almost nilpotent. Theorem 1 is deduced from the following proposition. Every soluble periodic group G of solvability class s having an automorphism of prime order p with precisely n fixed points contains a nilpotent subgroup H such that the nilpotency class of H and the index \(| G:H|\) are bounded by functions depending of p, n, s (Theorem 2).
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4083920
zbMATH Keywords: nilpotent periodic group
zbMATH Keywords: automorphism of prime order
zbMATH Keywords: locally soluble periodic group
zbMATH Keywords: nilpotent subgroup
author: Evgenii I. Khukhro
reviewed by: Ju. I. Merzljakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4083920