A Finite Simple Group Is Cca If And Only If It Has No Element Of Order Four

A Cayley graph for a group G is CCA if every automorphism of the graph that preserves the edge-orbits under the regular representation of G is an element of the normaliser of G. A group G is then said to be CCA if every connected Cayley graph on G is CCA. We show that a finite simple group is CCA if and only if it has no element of order 4. We also show that "many" 2-groups are non-CCA. (C) 2020 Elsevier Inc. All rights reserved.