On a strongly embedded infinitely isolated subgroup of a periodic group
type: Item
instance of: scholarly article
title: On a strongly embedded infinitely isolated subgroup of a periodic group
zbMATH Open document ID: 0546.20034
DOI: 10.1007/BF01978662
author: A. N. Izmajlov
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187211
review text: This is a continuation of a paper by the author and \textit{V. P. Shunkov} [Algebra Logika 21, 647-669 (1982; Zbl 0536.20022)]. It gives a further criterion for the non-simplicity of a group G having a strongly embedded infinite isolated subgroup H. It is assumed that H contains infinitely many involutions such that G has an involution for which the centralizer of any infinite subgroup without elements of order 2 contains a non- trivial element whose centralizer in that subgroup is infinite. Suppose also that H has a non-trivial element b that is strictly real relative to a certain involution of G whose centralizer in G is not contained in H. Then G has a normal Abelian subgroup B between H and \(\) that does not contain involutions such that all elements of B are strictly real relative to any involution in G. Also, G is the product of the centralizer of B and that of any involution in G, and the Sylow 2- subgroups are either locally cyclic or generalized quaternion groups.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 3869597
zbMATH Keywords: non-simplicity
zbMATH Keywords: strongly embedded infinite isolated subgroup
zbMATH Keywords: involutions
zbMATH Keywords: centralizer
zbMATH Keywords: normal Abelian subgroup
zbMATH Keywords: Sylow 2-subgroups
zbMATH Keywords: generalized quaternion groups
MaRDI profile type: Publication
cites work: Q5599233
cites work: Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt fest läßt
cites work: Q4745979
cites work: Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
OpenAlex ID: W2025084522
description: scientific article; zbMATH DE number 3869597