The spectrum for quasigroups with cyclic automorphisms and additional symmetries
| Autor: | Melinda Buchanan, Darryn Bryant, Ian M. Wanless |
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| Jazyk: | angličtina |
| Předmět: |
Discrete mathematics
Steiner triple system Mendelsohn triple system Totally symmetric Latin square Unipotent Diagonally cyclic Automorphism Theoretical Computer Science Combinatorics Mathematics::Group Theory Steiner system Idempotence Homogeneous space Order (group theory) Discrete Mathematics and Combinatorics Commutative property Quasigroup Mathematics Semi-symmetric |
| Zdroj: | Discrete Mathematics. (4):821-833 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2008.01.020 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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