On w- s-Permutable Subgroups of a Finite Group.

Let H be a subgroup of a group G. Then we say that H is w- s-permutable in G if G has a normal subgroup K such that HK is s-permutable in G and $$H\cap K$$ is nearly s-permutable in G. In this article, we analyse the structure of a group G by using the properties of w- s-permutable subgroups and obtain some new characterizations of p-nilpotent groups and supersoluble groups. Some known results are generalized. [ABSTRACT FROM AUTHOR]