## The Influence of Weakly s-supplemented Subgroups on Solvability of Finite Groups

**LU Jiakuan;QIU Yanyan;College of Mathematics and Statistics,Guangxi Normal University;**

A subgroup H of a finite group Gis called weakly s-supplemented subgroup of Gif there is a subgroup K of Gsuch that G=HK and H ∩K≤H_(sG),where H_(sG) is the subgroup of H generated by all those subgroups of H which are s-permutable in G.In this paper,the following results are proved:(1)a finite group Gis solvable if every subgroup of odd prime order of G is weakly s-supplemented in G;(2)a finite group Gis solvable if and only if every Sylow subgroup of odd order of Gis weakly ssupplemented in G.Some classical and recent results are extended.

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