Abstract In this paper we characterize those automorphism groups of colored graphs and digraphs that are abelian as abstract groups. This is done in terms basic permutation group properties. Using Schur’s classical terminology, what provide characterizations the classes 2-closed $$2^*$$ 2 ∗ </...

In recent years probabilistic methods have proved useful in the solution of several problems concerning finite groups, mainly involving simple groups and permutation groups. In some cases the probabilistic nature of the problem is apparent from its very formulation (see [KL], [GKS], [LiSh1]); but in other cases the use of probability, or counting, is not entirely anticipated by the nature of th...