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On central Frattini extensions of finite groups

Kovacs, L

Description

An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H. The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G if and only if A can be written as a direct product A = U × V such that U is a homomorphic image of...[Show more]

dc.contributor.authorKovacs, L
dc.date.accessioned2015-12-13T22:53:54Z
dc.identifier.issn0033-3883
dc.identifier.urihttp://hdl.handle.net/1885/82019
dc.description.abstractAn extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H. The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G if and only if A can be written as a direct product A = U × V such that U is a homomorphic image of the Schur multiplicator of G and the Frattini quotient of V is a homomorphic image of G.
dc.publisherKossuth Lajos Tudomanyegyetem
dc.sourcePublicationes Mathematicae Debrecen
dc.subjectKeywords: Finite groups; Frattini extensions
dc.titleOn central Frattini extensions of finite groups
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume67
dc.date.issued2005
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.ariespublicationMigratedxPub10319
local.type.statusPublished Version
local.contributor.affiliationKovacs, L, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue3-4
local.bibliographicCitation.startpage493
local.bibliographicCitation.lastpage497
dc.date.updated2015-12-11T11:00:35Z
local.identifier.scopusID2-s2.0-27344454440
CollectionsANU Research Publications

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