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The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Bryant, Darryn; Buchanan, Melinda; Wanless, Ian

Description

We determine necessary and sufficient conditions for the existence of a quasigroup of order n having an automorphism consisting of a single cycle of length m and n - m fixed points, and having any combination of the additional properties of being idempotent, unipotent, commutative, semi-symmetric or totally symmetric. Quasigroups with such additional properties and symmetries are equivalent to various classes of triple systems.

dc.contributor.authorBryant, Darryn
dc.contributor.authorBuchanan, Melinda
dc.contributor.authorWanless, Ian
dc.date.accessioned2015-12-07T22:23:48Z
dc.identifier.issn0012-365X
dc.identifier.urihttp://hdl.handle.net/1885/20873
dc.description.abstractWe determine necessary and sufficient conditions for the existence of a quasigroup of order n having an automorphism consisting of a single cycle of length m and n - m fixed points, and having any combination of the additional properties of being idempotent, unipotent, commutative, semi-symmetric or totally symmetric. Quasigroups with such additional properties and symmetries are equivalent to various classes of triple systems.
dc.publisherElsevier
dc.sourceDiscrete Mathematics
dc.subjectKeywords: System theory; Diagonally cyclic; Latin square; Mendelsohn triple system; Quasigroup; Semi-symmetric; Steiner triple system; Totally symmetric; Equivalence classes Diagonally cyclic; Latin square; Mendelsohn triple system; Quasigroup; Semi-symmetric; Steiner triple system; Totally symmetric
dc.titleThe spectrum for quasigroups with cyclic automorphisms and additional symmetries
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume309
dc.date.issued2009
local.identifier.absfor010104 - Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
local.identifier.ariespublicationu4708487xPUB14
local.type.statusPublished Version
local.contributor.affiliationBryant, Darryn, University of Queensland
local.contributor.affiliationBuchanan, Melinda, University of Queensland
local.contributor.affiliationWanless, Ian, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage821
local.bibliographicCitation.lastpage833
local.identifier.doi10.1016/j.disc.2008.01.020
dc.date.updated2016-02-24T11:20:32Z
local.identifier.scopusID2-s2.0-60149098156
local.identifier.thomsonID000264620200021
CollectionsANU Research Publications

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