Skew product groups for monolithic groups

Source abstract

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool for the study of regular Cayley maps and, more generally, for finite groups with a complementary factorisation G = B Y , where Y is cyclic and core-free in G . In this paper, we classify all examples in which B is monolithic (meaning that it has a unique minimal normal subgroup, and that subgroup is not abelian) and core-free in G . As a consequence, we obtain a classification of all proper skew morphisms of finite non-abelian simple groups.