Groups with many subnormal subgroups
type: Item
instance of: scholarly article
title: Groups with many subnormal subgroups
zbMATH Open document ID: 1027.20012
DOI: 10.1016/S0021-8693(03)00095-4
author: Eloisa Detomi
published in: Journal of Algebra
publication date: 2003-07-30T00:00:00Z
review text: According to a classical result of Roseblade there is a function \(\rho\) such that all groups with all subgroups subnormal of defect at most \(n\) are nilpotent of class at most \(\rho(n)\). The groups considered here have the property that all subgroups containing a fixed finite subgroup \(F\) are subnormal of defect at most \(n\). Main results: If \(G\) is locally nilpotent, there is a function \(\beta\) such that \(G_{\beta(n)}\) is finite (and so \(G\) is nilpotent of a class depending on \(n\) and \(o(F)\)). -- If \(G\) is a torsion group and only finitely many primes \(p\) are orders of group elements, then \(G_{\beta(n)}\) is finite (Theorems 0.2 and 0.3). The finiteness of the set of primes is indispensable; this is shown by a counterexample.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 1956740
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: generalized nilpotency
zbMATH Keywords: nilpotency classes
zbMATH Keywords: defect
zbMATH Keywords: locally nilpotent groups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00095-4
OpenAlex ID: W2038077494
description: scientific article; zbMATH DE number 1956740