有限群为B_p群的两个充分条件  

Two Sufficient Conditions for a Finite Group as B p Group

作　　者：涂道兴 

出　　处：《西南石油学院学报》1996年第4期107-109,共3页Journal of Southwest Petroleum Institute

摘　　要：设Ｇ为有限群，π为某素数集合。Ｇ的子群Ｈ称为Ｇ的π—Ｓ—拟正规子群，如果对每个Ｐ∈π，Ｈ与Ｇ的每个ＳｙｌｏｗＰ—子群可换。Ｇ称为Ｂｐ群，如果ＮＧ（Ｐ）为Ｐ－幂零群蕴含Ｇ为Ｐ－幂零群，其中Ｐ∈ＳｙｌｐＧ。本文证明了Ｇ为Ｐｐ群，如果Ｇ满足下列条件之一：（１）Ｇ的ＳｙｌｏｗＰ—子群Ｐ的每个极大子群为Ｇ的ｐ—Ｓ—拟正规子群；（２）Ｇ的ＳｙｌｏｗＰ—子群Ｐ的每个二次极大子群为Ｇ的ｐ—Ｓ—拟正规子群。et G be a finite group, and let be a set of primes. A subgroup H of G is called π-S-quasi-normal in G if H is permuted with every Sylow p-subgroup of G for every p in π. G is called a B p group if the existence of normal p-complements of N (P) implies that G itself as a normal p-complement, where PE Sylp G . In this paper, we have proved that G is a B p group if G satisfies one of the following conditions: (1) each maximal subgroup of a Sylow p-subgroup P of G is P'-S-quasi-mormal in G ; (2) each second maximal subguoup of a Sylow p-subgroup P of G is p'-S-quasi-normal in G .

关 键 词：有限群 西洛子群 正规子群 

分 类 号：O152.1[理学—数学]