Some sufficient conditions for a finite group to be supersolvable

This paper represents an attempt to extend and improve the following result of Berkovich: Let G be a group of odd order. Let G=G 1G 2 such that G 1 and G 2 are subgroups of G. If the Sylow p-subgroups of G 1 and of G 2 are cyclic, then G is p-supersolvable. © 2011 Akadémiai Kiadó, Budapest, Hungary.