On conditional permutability and factorized groups.
type: Item
instance of: scholarly article
title: On conditional permutability and factorized groups.
zbMATH Open document ID: 1321.20019
author: Ana Martínez-Pastor
author: M. Arroyo-Jordá
author: Paz Arroyo-Jordá
author: M. D. Pérez-Ramos
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2014-09-11T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/61370
review text: Two subgroups \(A,B\) of a finite group \(G\) are called tcc-permutable if for all pairs of subgroups \(X\subseteq A\) and \(Y\subseteq B\) there is an element \(g\in\langle X,Y\rangle\) such that \(X\) permutes with \(Y^g\). This is a generalization of total permutability. The authors show that certain results following from total permutability are still true for tcc-permutability. For instance, if \(G=G_1\cdots G_k\) is the product of pairwise tcc-permutable subgroups \(G_j\) and \(F\) is a saturated formation containing all supersoluble groups, then \(G_j\in F\) for all \(j\) and \(G\in F\) are equivalent (Theorem 5).
reviewed by: Hermann Heineken
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 6342896
zbMATH Keywords: finite groups
zbMATH Keywords: products of subgroups
zbMATH Keywords: conditional permutability
zbMATH Keywords: saturated formations
zbMATH Keywords: completely conditionally permutable subgroups
MaRDI profile type: Publication
OpenAlex ID: W2063630538
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DOI: 10.1007/S10231-012-0319-1
description: scientific article; zbMATH DE number 6342896