Influence of Mp-supplemented subgroups on the structure of p-modular subgroups

Аннотация

A subgroup K of G is M_p-supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = p^α. We study the structure of the chief factor of G by using M_p-supplemented subgroups and generalize the results of Monakhov and Shnyparkov by involving the relevant results about the p-modular subgroup O^p(G) of G.