Regular Permutation Groups and Cayley Graphs

Speaker: Cheryl E. Praeger

Date: Fri, Jul 10, 2009

Location: University of New South Wales, Sydney, Australia

Conference: 1st PRIMA Congress

Subject: Mathematics, Group Theory

Class: Scientific


Regular permutation groups are the `smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as subgroups of automorphisms of Cayley graphs, and their applications range from obvious graph theoretic ones through to studying word growth in groups and modeling random selection for group computation. Recent work, using the finite simple group classification, has focused on the problem of classifying the finite primitive permutation groups that contain regular permutation groups as subgroups, and classifying various classes of vertex-primitive Cayley graphs. Both old and very recent work on regular permutation groups will be discussed.