On finite groups with some primary subgroups satisfying partial S-Pi-property

摘要

A p-subgroup H of a finite group G is said to satisfy partial S-Pi-property in G if G has a chief series Gamma(G) : 1 = G(0) < G(1) < ... < Gn =G such that for every G-chief factor G(i)/G(i-1) (1 <= i <= n) of Gamma(G), either (H boolean AND G(i))G(i-1) is a Sylow p-subgroup of G(i)/G(i-1) or vertical bar G/G(i-1) : N-G/G(i-1) (H boolean AND G(i))G(i-1)/G(i-1) is a p-number. In this paper, we mainly investigate the structure of finite groups with some primary subgroups satisfying partial S-Pi-property.