Groups with a supersoluble triple factorization
type: Item
instance of: scholarly article
title: Groups with a supersoluble triple factorization
zbMATH Open document ID: 0646.20026
DOI: 10.1016/0021-8693(88)90245-1
author: Silvana Franciosi
author: F. de Giovanni
author: Bernhard Amberg
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: This paper studies groups G which have a triple factorization, a situation which often arises in the study of groups which are expressible as a product of two of their subgroups. That is, \(G=AB=AK=BK\), where A and B are subgroups and K is a normal subgroup of G. The main results all concern the situation where K is hypercentral and this is assumed in their statements below: Theorem A. If A and B are supersoluble then G is supersoluble. - Theorem B. (a) If A and B are locally supersoluble and K is minimax, then G is locally supersoluble. (b) If A and B are hypercyclic and K is minimax, then G is hypercyclic. - Theorem C. If G has finite abelian section rank and A and B are locally supersoluble, then G is locally supersoluble and hence hypercyclic. - The authors give examples to show what limits there are on possible generalizations of these results.
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 4053902
zbMATH Keywords: product of subgroups
zbMATH Keywords: triple factorization
zbMATH Keywords: hypercentral
zbMATH Keywords: locally supersoluble
zbMATH Keywords: minimax
zbMATH Keywords: hypercyclic
zbMATH Keywords: finite abelian section rank
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90245-1
OpenAlex ID: W2073193819
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description: scientific article; zbMATH DE number 4053902