On Generalized PST-groups

A finite group G is called a generalized PST-group if every subgroup contained in F(G)permutes all Sylow subgroups of G,where F(G)is the Fitting subgroup of G.The class of generalized P ST-groups is not subgroup and quotient group closed,and it properly contains the class of P ST-groups.In this paper,the structure of generalized P ST-groups is first investigated.Then,with its help,groups whose every subgroup(or every quotient group)is a generalized P ST-group are determined,and it is shown that such groups ...