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Suppose that is a finite group and is a subgroup of . Subgroup is said to be weakly -supplemented in if there exists a subgroup of such that (1) , and (2) if is a maximal subgroup of , then , where is the largest normal subgroup of contained in . We fix in every noncyclic Sylow subgroup of a subgroup satisfying and study the -nilpotency of under the assumption that every subgroup of with is weakly -supplemented in . Some recent results are generalized.
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