On the rarity of quasinormal subgroups
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 0041-8994Full text not available from this repository.
Official URL: http://rendiconti.math.unipd.it/volumes/vol125.php...
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|
|Page Range:||pp. 81-105|
|Access rights to Published version:||Restricted or Subscription Access|
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