Groups of Heineken-Mohamed
type: Item
instance of: scholarly article
title: Groups of Heineken-Mohamed
zbMATH Open document ID: 0822.20029
author: F. Menegazzo
published in: Journal of Algebra
publication date: 1995-10-10T00:00:00Z
review text: The groups of the title are non-nilpotent groups all of whose proper subgroups are both nilpotent and subnormal, we abbreviate to H-M-groups. The author shows: (I) There are H-M \(p\)-groups with trivial centre and commutator subgroups abelian of infinite exponent (Theorem 2.3). Hartley gave examples with abelian commutator subgroups of finite exponent. (II) There are H-M \(p\)-groups with \(G'\) of derived length \(d\) for every \(d\) (Theorem 3.7). By considering multipliers Bruno and Phillips showed how to construct groups with \(G'\) of nilpotency class 2. By the exhibited constructions the collection of known such groups is widened considerably.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 735326
zbMATH Keywords: normalizer condition
zbMATH Keywords: nilpotent subgroups
zbMATH Keywords: H-M-groups
zbMATH Keywords: \(p\)-groups
zbMATH Keywords: commutator subgroups
zbMATH Keywords: derived length
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: jabr.1995.1037
OpenAlex ID: W2001805232
DOI: 10.1006/JABR.1995.1037
description: scientific article; zbMATH DE number 735326