Sylow theory of CC-groups
type: Item
instance of: scholarly article
title: Sylow theory of CC-groups
zbMATH Open document ID: 0734.20016
author: J. M. Peña
author: Javier Otal
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1991-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108210
review text: \(G\) is a CC-group if \(G/C_ G(x^ G)\) is a Chernikov group. Results on Sylow \(p\)-subgroups of CC-groups were obtained by \textit{J. Alcazar} and \textit{J. Otal} [J. Algebra 110, No. 2, 507--513 (1987; Zbl 0624.20026)]. Here Sylow \(\pi\)-subgroups, Sylow bases and Carter subgroups (self-normalizing locally nilpotent subgroups) of periodic locally soluble CC-groups are considered and local conjugacy theorems are proved. Finally a large number of conditions equivalent to the conjugacy of Carter subgroups are obtained. For example, the following are equivalent: (a) the Carter subgroups of \(G\) are conjugate, (b) \(G\) has countable many Carter subgroups (c) the Sylow bases of \(G\) are conjugate, (d) \(G\) is (locally nilpotent)-by-finite.
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 4214252
zbMATH Keywords: Chernikov group
zbMATH Keywords: Sylow p-subgroups
zbMATH Keywords: CC-groups
zbMATH Keywords: Sylow \(\pi\)-subgroups
zbMATH Keywords: Sylow bases
zbMATH Keywords: self-normalizing locally nilpotent subgroups
zbMATH Keywords: periodic locally soluble CC-groups
zbMATH Keywords: local conjugacy theorems
zbMATH Keywords: conjugacy of Carter subgroups
zbMATH Keywords: (locally nilpotent)-by-finite
reviewed by: M. J. Tomkinson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4214252