π-Fratini子群与π-局部群系(英文)

π Frattini Subgroup and π Local Formation

英文关键词:π-Frattini subgroup  π-locally defined formation  Gaschütz theorem.

中文摘要:

      文中，对π－Ｆｒａｔｉｎｉ子群给出了更精细的结果，并将Ｇａｓｃｈüｔｚ幂零性定理推广到π－局部定义群系．主要结果是：设Ｇ为有限群，Ｈ为Ｇ的次正规子群．若Ｈ／Ｈ∩Φ（Ｇ）Ｏπ′（Ｇ）∈Ｆ，则Ｈ∈Ｆπ，其中Ｆπ是π－可解π－局部定义群系．

英文摘要:

      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.