Cultural advice

The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

Aboriginal and Torres Strait Islander peoples are advised that ANU Library collections may include images, names, voices, and other representations of deceased persons.

Material in the collection may contain terms, language or views that reflect the period in which the item was created and may be considered inappropriate today.

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

Date

Authors

Bryant, Darryn

Buchanan, Melinda

Wanless, Ian

Publisher

Elsevier

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.

Keywords

Keywords: 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

URI

http://hdl.handle.net/1885/20873

Collections

ANU Research Publications

Source

Discrete Mathematics

Type

Journal article

DOI

10.1016/j.disc.2008.01.020

Restricted until

2037-12-31

Downloads

File

Description

01_Bryant_The_spectrum_for_quasigroups_2009.pdf (657.11 KB)

abcd