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

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Recent work of Gromov, Epstein, Cannon, Thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups. (See [16],[17] and [14].) Many of these structures are preserved by taking graph products. The graph product of groups (not to be confused with the fundamental group of a graph of groups) is a product mixing direct and f...