On the Rarity of Quasinormal Subgroups
Cossey, Peter (John); Stonehewer, Stewart Edward
Description
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 pn-1 and X is a cyclic subgroup of order pn. 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...[Show more]
dc.contributor.author | Cossey, Peter (John) | |
---|---|---|
dc.contributor.author | Stonehewer, Stewart Edward | |
dc.date.accessioned | 2015-12-07T22:25:29Z | |
dc.identifier.issn | 0041-8994 | |
dc.identifier.uri | http://hdl.handle.net/1885/21312 | |
dc.description.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 pn-1 and X is a cyclic subgroup of order pn. 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, pn-2 or pn-1. Those of exponent p are nested and they all lie in each of those of exponent pn-2 and pn-1. | |
dc.publisher | Australian National University | |
dc.source | Rendiconti del Seminario della Universita di Padova | |
dc.title | On the Rarity of Quasinormal Subgroups | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 125 | |
dc.date.issued | 2011 | |
local.identifier.absfor | 010105 - Group Theory and Generalisations | |
local.identifier.ariespublication | u4685828xPUB16 | |
local.type.status | Published Version | |
local.contributor.affiliation | Cossey, Peter (John), College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Stonehewer, Stewart Edward, University of Warwick | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 81 | |
local.bibliographicCitation.lastpage | 105 | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
dc.date.updated | 2015-12-07T09:37:07Z | |
local.identifier.scopusID | 2-s2.0-84856162940 | |
local.identifier.thomsonID | 000294886300006 | |
Collections | ANU Research Publications |
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