Groups of automorphisms with TNI-centralizers
type: Item
instance of: scholarly article
title: Groups of automorphisms with TNI-centralizers
zbMATH Open document ID: 1425.20011
author: Gülin Ercan
author: İsmail Ş. Güloğlu
published in: Journal of Algebra
publication date: 2018-02-06T00:00:00Z
review text: A number of results give information about a finite group $G$, when we are given a finite group $A$ of automorphisms of $G$, and some further information. This information on $G$ is particularly strong when $C_G(A) = 1$. The authors obtain similar results when the condition that $C_G(A) = 1$ is weakened to the condition that $C_G(A)$ is a TNI-subgroup of $G$. A subgroup $H$ of a finite group $G$ is a TNI-subgroup if, for all $g \in G$ if $g \notin N_G(H)$ then $N_G(H) \cap H^g = 1$. For example, the authors show that, if $C_G(A)$ is a TNI-subgroup of $G$, then $G$ is solvable if and only if $C_G(A)$ is solvable. Furthermore they find some bounds on the nilpotent length of $G$ in terms of the nilpotent length of $C_G(A)$ under some further conditions. They also consider in more detail the case when $A$ is a Frobenius group.
reviewed by: Alexandre Turull
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 6834820
zbMATH Keywords: TNI-subgroup
zbMATH Keywords: automorphism
zbMATH Keywords: centralizer
zbMATH Keywords: Frobenius group
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2017.10.021
OpenAlex ID: W2768142077
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DOI: 10.1016/J.JALGEBRA.2017.10.021
description: scientific article; zbMATH DE number 6834820