Representing finite groups as regular automorphism groups of combinatorial structures
by
Robert Jajcay
Indiana State University, Terre Haute, IN 47809, U.S.A.

Given a regular action of a finite group G on a set V , we consider the problem of the existence of an incidence structure I = ( V, B) on the set V whose full automorphism group Aut(I) is the group G in its regular action. Using results on graphical and digraphical regular representations we have been able to show the existence of such an incidence structure for all but four small finite groups.

Additional conditions on I further allow us to refine the original problem to the class of hypergraphs. We shall also investigate an interesting connection between complete Cayley maps and t-designs with regular automorphism groups.

Date received: November 8, 2000