Groups with an FC-nilpotent triple factorization
type: Item
instance of: scholarly article
title: Groups with an FC-nilpotent triple factorization
zbMATH Open document ID: 0672.20013
published in: Ricerche di Matematica
publication date: 1987-01-01T00:00:00Z
review text: The authors study groups G which have a triple factorization \(G=AB=AK=BK\) where A and B are subgroups, and K is a normal subgroup of G. Triple factorizations are important in the study of groups that are expressed as the product of a pair of subgroups. Let G be a group with a triple factorization \(G=AB=AK=BK\) in which K is a minimax group. Theorem: If A and B are FC-nilpotent, then so is G. Here ``FC-nilpotent'' can be replaced by ``FC-hypercentral'' and ``locally FC-nilpotent''. A similar result is proved for the case where G has finite abelian section rank and no hypothesis is placed on K.
reviewed by: Derek J. S. Robinson
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20F24
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 4099550
zbMATH Keywords: Triple factorizations
zbMATH Keywords: minimax group
zbMATH Keywords: locally FC-nilpotent
zbMATH Keywords: abelian section rank
author: Bernhard Amberg
author: Silvana Franciosi
author: F. de Giovanni
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4099550