Produkte von Gruppen mit endlichem torsionsfreien Rang
type: Item
instance of: scholarly article
title: Produkte von Gruppen mit endlichem torsionsfreien Rang
zbMATH Open document ID: 0552.20013
DOI: 10.1007/BF01195364
author: Bernhard Amberg
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: The following theorem is proved: Let the group G have a finite normal series with abelian or periodic factors. If the group \(G=AB\) is the product of two subgroups A and B with finite torsionfree ranks \(r_ 0(A)\) and \(r_ 0(B)\) and if the hypercenter of A has finite index in A, then G has finite torsionfree rank \(r_ 0(G)\leq r_ 0(A)+r_ 0(B)-r_ 0(A\cap B)\). - This generalizes a result of D. I. Zajtsev and uses some of his methods. It remains open whether the inequality can be replaced by equality.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 3879135
zbMATH Keywords: finite normal series
zbMATH Keywords: abelian or periodic factors
zbMATH Keywords: product of two subgroups
zbMATH Keywords: torsionfree rank
zbMATH Keywords: hypercenter
MaRDI profile type: Publication
cites work: Artinian and Noetherian factorized groups
cites work: Factorizations of infinite soluble groups
cites work: Über das Produkt von zwei abelschen Gruppen
cites work: On the solvability of some factorized linear groups
cites work: Q3663506
cites work: Q3905468
full work available at URL: https://doi.org/10.1007/bf01195364
OpenAlex ID: W2014863377
description: scientific article; zbMATH DE number 3879135