中文摘要：

称有限群G的子群H为弱s-可补子群，如果存在G的子群K，使得G=HK，HnK≤Hm，其中H，G是由H的在G中s-置换的子群生成的子群。本文证明了如下结果：①如果有限群G的奇素数阶子群在G中弱s-可补，那么G是可解群；②有限群G是可解群当且仅当G的所有奇数阶Sylow子群在G中弱s-可补。这2个结果推广和改进了已有的结果。

英文摘要：

A subgroup H of a finite group G is called weakly s-supplemented subgroup of G if there is a subgroup K of G such that G=HK and H ∩K≤HsG, where HsG 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 G is solvable if every subgroup of odd prime order of G is weakly s-supplemented in G; （2） a finite group G is solvable if and only if every Sylow subgroup of odd order of G is weakly s- supplemented in G. Some classical and recent results are extended.