Abstract
Let G be a finite group, H a subgroup of G and p a prime number. We say that H is weakly sp-permutable in G if G has a subnormal subgroup K such that G = HK, and
is a
-number, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. In this paper, we investigate the structure of a group G under the assumption that certain subgroups of G are weakly sp-permutable in G. Some recent results are extended and generalized.
Communicated by Alexander Olshanskii
Acknowledgment
The authors are very grateful for the helpful suggestions of the referee.