Supersolvability of finite factorizable groups with cyclic Sylow subgroups in the factors

Abstract

Let p be a prime. Under certain additional conditions, we establish the p-supersolvability of a finite p-solvable group G = AB with cyclic Sylow p-subgroups in A and B. In particular, we prove that a finite group G = AB is supersolvable provided that all Sylow subgroups in A and B are cyclic and either G is 2-closed or A and B are maximal subgroups.