A note on locally graded groups
type: Item
instance of: scholarly article
title: A note on locally graded groups
zbMATH Open document ID: 0852.20020
author: P. Longobardi
author: M. Maj
author: Howard Smith
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1996-12-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108376
review text: A group \(G\) is locally graded if every non-trivial finitely generated subgroup of \(G\) has a non-trivial finite image. The class of locally graded groups is clearly not closed under forming homomorphic images. Thus it is interesting to know when a homomorphic image of a locally graded group is likewise locally graded. The authors prove that if \(G\) is locally graded and \(H\) is a \(G\)-invariant subgroup of the Hirsch-Plotkin radical of \(G\), then also \(G/H\) is locally graded. As a corollary it turns out, that if \(H\) is a soluble normal subgroup of the locally graded group \(G\), then \(G/H\) is locally graded.
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 889843
zbMATH Keywords: finitely generated subgroups
zbMATH Keywords: finite images
zbMATH Keywords: locally graded groups
zbMATH Keywords: homomorphic images
zbMATH Keywords: Hirsch-Plotkin radical
zbMATH Keywords: soluble normal subgroups
reviewed by: Silvana Franciosi
MaRDI profile type: Publication
cites work: On homomorphic images of locally graded groups
description: scientific article; zbMATH DE number 889843