π-超可解群的弱拟正规

Weakly-Quasinormality of π-Supersolvable Group

引入有限群的弱拟正规子群的概念 ,利用这一概念获得了 π-可解群为 π-超可解群的一个充分条件 ,即若有限π-可解群 G的每个极大子群在 G中弱拟正规 ,则 G为π-超可解群 ,并给出反例指出该结论与超可解群中相应结论的不同之处。本文所提及的群都是有限的 ,所用的符号和概念也是规范的。

Weakly quasinormal subgroup of finite group is introduced and it is a generalization of quasinormal subgroup of finite group. A sufficient condition is obtained as follows: let G be a finite π solvable group, if every maximal subgroup of G is weakly quasinormal in G , then G is π supersolvable. An example shows that the result is different from the corresponding result of supersolvable group. The finite group is considered only. The standard notation and the terminology are used.