1.Department of Mathematics,Chonnam National University,Gwangju,Republic of Korea;2.Department of Mathematics,Iowa State University,Ames,USA
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.