Abstract
A subgroup H of a group G is called an -subgroup of G if
where
and
is the Frattini subgroup of
and HsG is the largest s-permutable subgroup of G contained in H. In this paper, we investigate the structure of finite group G under the assumption that some subgroups of G are
-subgroups of G, some results are obtained.
Acknowledgement
The authors are grateful to the referee for valuable comments and detailed corrections.