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On the rarity of quasinormal subgroups
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Cossey, John and Stonehewer, Stewart E. (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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Official URL: http://rendiconti.math.unipd.it/volumes/vol125.php...
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.125 | ||||
Page Range: | pp. 81-105 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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