Cossey, John, 1941- and Stonehewer, Stewart E. (Stewart Edward), 1935-. (2011) On the rarity of quasinormal subgroups. Rendiconti del Seminario Matematico della Università di Padova, Vol.125 . pp. 81-105. ISSN 0041-8994

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Abstract

For each prime p and positive integer n, Berger and Gross have defined a finite p-group G = HX, where H is a core-free quasinormal subgroup of exponent p(n-1) and X is a cyclic subgroup of order p(n). These groups are universal in the sense that any other finite p-group, with a similar factorisation into subgroups with the same properties, embeds in G. In our search for quasinormal subgroups of finite p-groups, we have discovered that these groups G have remarkably few of them. Indeed when p is odd, those lying in H can have exponent only p, p(n-2) or p(n-1). Those of exponent p are nested and they all lie in each of those of exponent p(n-2) and p(n-1).

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Group theory
Journal or Publication Title:	Rendiconti del Seminario Matematico della Università di Padova
Publisher:	C E D A M
ISSN:	0041-8994
Date:	2011
Volume:	Vol.125
Page Range:	pp. 81-105
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/38147

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