In this paper, our purpose is to make the results about π Frattini subgroup more accurate, and to extend Gaschütz Theorem about nilpotency to π locally defined formation. We come to Theorem L...In this paper, our purpose is to make the results about π Frattini subgroup more accurate, and to extend Gaschütz Theorem about nilpotency to π locally defined formation. We come to Theorem Let G be a finite group, H a subnormal subgroup of G. If H/H∩Φ(G)O π′ (G)∈F, then H∈F π, where F π is π solvable π locally defined formation.展开更多
文摘In this paper, our purpose is to make the results about π Frattini subgroup more accurate, and to extend Gaschütz Theorem about nilpotency to π locally defined formation. We come to Theorem Let G be a finite group, H a subnormal subgroup of G. If H/H∩Φ(G)O π′ (G)∈F, then H∈F π, where F π is π solvable π locally defined formation.
基金supported by the National Natural Science Foundation of China(Nos.11771129,11301150,11601121)the Natural Science Foundation of Henan Province of China(No.162300410066)
文摘Let G be a finite p-group with a cyclic Frattini subgroup. In this paper, the automorphism group of G is determined.
