摘要
本文证明了下面主要结果定理１设Ｇ是ｎ－可解群，π是一些素数之集，若对任意ｐ∈π∩π（Ｇ），（ｐ，ｎ（１－ｎ））＝１，则Ｇ的π－Ｈａｌ子群的个数ｒ＝ｋ１ｋ２…ｋｔ，每ｋｉ≡１（ｍｏｄｐ），某ｐ∈π，且每ｋｉ整除Ｇ的一个主因子．定理３设Ｇ是有限群，Ｈ是Ｇ的ｎ－幂零π－Ｈａｌ子群，若Ｍ是Ｇ的π－子群，ｐ（｜Ｍ｜，ｎ（１－ｎ））＝１，则存在ｇ∈Ｇ使Ｍｇ≤Ｈ．
In this paper, we prove the following theorems: Theorem 1 Let G be a n solvable group, π be a set of promes. If (p,n(1-n))=1 for all p∈π∩π(G) , then the number of Hall π subgroups of G is r=k 1k 2…k t,k i≡1 (mod p ). for some p∈π and k i divides a chief factor of G. Theorem 3 Let G be a finite group, H be a n nilpotent Hall π subgroup of G. If M is a π subgroup of G With (|M|,n(1-n))=1 , then there exists g∈G such that M g≤H.
出处
《数学杂志》
CSCD
1997年第4期445-449,共5页
Journal of Mathematics
