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Generalising quasinormal subgroups
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Stonehewer, Stewart E. (2012) Generalising quasinormal subgroups. Bulletin of the Australian Mathematical Society , Volume 86 (Number 1). pp. 1-10. doi:10.1017/S0004972711003376 ISSN 0004-9727 .
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Official URL: http://dx.doi.org/10.1017/S0004972711003376
Abstract
In Cossey and Stonehewer ['On the rarity of quasinormal subgroups', Rend. Semin. Mat. Univ. Padova 125 (2011), 81-105] it is shown that for any odd prime p and integer n >= 3, there is a finite p-group G of exponent p(n) containing a quasinormal subgroup H of exponent p(n-1) such that the nontrivial quasinormal subgroups of G lying in H can have exponent only p, p(n-1) or, when n >= 4, p(n-2). Thus large sections of these groups are devoid of quasinormal subgroups. The authors ask in that paper if there is a nontrivial subgroup-theoretic property X: of finite p-groups such that (i) X is invariant under subgroup lattice isomorphisms and (ii) every chain of X-subgroups of a finite p-group can be refined to a composition series of X-subgroups. Failing this, can such a chain always be refined to a series of X-subgroups in which the intervals between adjacent terms are restricted in some significant way? The present work embarks upon this quest.
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): | Finite groups | ||||
Journal or Publication Title: | Bulletin of the Australian Mathematical Society | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0004-9727 | ||||
Official Date: | August 2012 | ||||
Dates: |
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Volume: | Volume 86 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 1-10 | ||||
DOI: | 10.1017/S0004972711003376 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 23 December 2015 | ||||
Date of first compliant Open Access: | 23 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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