The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Bryant, D., Buchanan, M. and Wanless, I. M. (2009) The spectrum for quasigroups with cyclic automorphisms and additional symmetries. Discrete Mathematics, 309 4: 821-833. doi:10.1016/j.disc.2008.01.020


Author Bryant, D.
Buchanan, M.
Wanless, I. M.
Title The spectrum for quasigroups with cyclic automorphisms and additional symmetries
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2009-03-01
Year available 2009
Sub-type Article (original research)
DOI 10.1016/j.disc.2008.01.020
Open Access Status Not yet assessed
Volume 309
Issue 4
Start page 821
End page 833
Total pages 13
Editor D. B. West
Place of publication Netherlands
Publisher Elsevier B. V.
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Abstract 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. (C) 2008 Elsevier B.V. All rights reserved.
Formatted abstract
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 nm 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.

Keyword Diagonally cyclic
Quasigroup
Latin square
Steiner triple system
Mendelsohn triple system
Semi-symmetric
Totally symmetric
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Sat, 22 Aug 2009, 01:42:50 EST by Marie Grove on behalf of School of Mathematics & Physics