The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Darryn Bryant; Melinda Buchanan; Ian M. Wanless

doi:10.1016/j.disc.2008.01.020

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Darryn Bryant^*, Melinda Buchanan, Ian M. Wanless

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

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.

Original language	English
Pages (from-to)	821-833
Number of pages	13
Journal	Discrete Mathematics
Volume	309
Issue number	4
DOIs	https://doi.org/10.1016/j.disc.2008.01.020
Publication status	Published - 6 Mar 2009
Externally published	Yes

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10.1016/j.disc.2008.01.020

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AU - Wanless, Ian M.

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AB - 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.

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KW - Latin square

KW - Mendelsohn triple system

KW - Quasigroup

KW - Semi-symmetric

KW - Steiner triple system

KW - Totally symmetric

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DO - 10.1016/j.disc.2008.01.020

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 4

ER -

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Abstract

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