Abstract:

Using the Mpembedding properties of some primary subgroup of Fitting subgroup and generalized Fitting subgroup to study the structure of finite groups, we obtained some sufficient conditions of supersolvable groups. At the same time, it was found that Mpembedding properties of subgroups have important influence on the structure of finite groups.

Key words: M_p-embedded subgroup, saturated formation, finite group, supersoluble group