Abstract
A subgroup H is called to be nearly -supplemented in G if G has a normal subgroup K such that HK ⊴ G and for every maximal subgroup Hi of H. The main goal of this paper is to investigate the structure of chief factors of finite groups by using nearly -supplemented primary subgroups and obtain some new characterization about chief factors of finite groups. The main result is the following: Let and P be a Sylow p-subgroup of G, where p is an odd prime. If every maximal subgroup of P is nearly -supplemented in G, then every non-abelian pd-G-chief factor A/B satisfies one of the following conditions:
and p = 7; and p = 11;
and is a Fermat prime;
is a prime, and ;
and p = 11; and p = 23;
and .
Acknowledgements
We thank the reviewers for their suggestions which have helped to improve our original version.