Sharply transitive sets in quasigroup actions
Bokhee Im
, Ji-Young Ryu
and Jonathan D.H. Smith
DOI: 10.1007/s10801-010-0234-8
Abstract
This paper forms part of the general development of the theory of quasigroup permutation representations. Here, the concept of sharp transitivity is extended from group actions to quasigroup actions. Examples of nontrivial sharply transitive sets of quasigroup actions are constructed. A general theorem shows that uniformity of the action is necessary for the existence of a sharply transitive set. The concept of sharp transitivity is related to two pairwise compatibility relations and to maximal cliques within the corresponding compatibility graphs.
Pages: 81–93
Keywords: keywords sharply transitive; sharp transitivity; simply transitive; uniformly transitive; permutation group; permutation action; group action; quasigroup action; Lagrange theorem; permutation graph; maximal clique
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References
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4. Godsil, C., Meagher, K.: A new proof of the Erd\Acute\Acute os-Ko-Rado theorem for intersecting families of permutations.
5. Heinrich, K., Wallis, W.D.: The maximum number of intercalates in a Latin square. In: McAvaney, K.L. (ed.) Combinatorial Mathematics VIII, pp. 221-233. Springer, Berlin (1981)
6. Johnson, K.W., Smith, J.D.H.: Characters of finite quasigroups. Eur. J. Comb. 5, 43-50 (1984)
7. Johnson, K.W., Smith, J.D.H.: Characters of finite quasigroups II: induced characters. Eur. J. Comb. 7, 131-137 (1986)
8. Johnson, K.W., Smith, J.D.H.: Characters of finite quasigroups III: quotients and fusion. Eur. J. Comb.
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