Hall chains in normal subgroups of finite \(p\)-groups.
type: Item
instance of: scholarly article
title: Hall chains in normal subgroups of finite \(p\)-groups.
zbMATH Open document ID: 1165.20014
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: Let \(G\) be a finite \(p\)-group, and \(H\) a normal subgroup of \(G\). A \(k\)-admissible chain in \(H\) is a chain \(\{1\}=L_0<L_1<\cdots<L_n=H\) of \(G\)-invariant subgroups such that each quotient group \(L_i/L_{i-1}\) has order at most \(p^k\) and exponent \(p\). Various questions about the existence of such chains are studied. In particular, Abelian \(p\)-groups with exactly one such chain are characterised, and metacyclic 2-groups without any such chain for \(k=2\) are classified.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 5508714
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: Hall chains
zbMATH Keywords: chains of normal subgroups
author: Yakov Berkovich
reviewed by: Andrea Caranti
MaRDI profile type: Publication
full work available at URL: s11856-008-1055-5
OpenAlex ID: W1996798043
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DOI: 10.1007/S11856-008-1055-5
description: scientific article; zbMATH DE number 5508714