We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a fin...We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a finite group C is solvable if and only if G has a Hall p/-subgroup for every prime p.展开更多
基金supported by NSFC(Grant No.11471054)supported by NSFC(Grant No.11101055)
文摘We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a finite group C is solvable if and only if G has a Hall p/-subgroup for every prime p.
