摘要
讨论了当N≤｜G时,IBrp(G｜N)对正规子群N的结构及N对G的扩张性质的影响.得到: 定理1 若N G,G/N是p′群,则对任意的非线性不可约pBrauer特征标φ∈IBrp(G｜N)有:素数p不 整除φ(1)当且仅当N有正规Sylowp子群. 定理3 设G是p可解群,G/N是{p,q}′群,N G,素数p≠q.若对所有非线性不可约pBrauer特征标 φ∈IBrp(G｜N)有q｜φ(1),则N有一正规q补. 定理4 设G是p可解群,G/N是p′群,N G.素数p≠q.若对所有非线性不可约pBrauer特征标φ∈ IBrp(G｜N′)有q｜φ(1),则N有一正规q补.
In this paper the effect of IBr_p(G｜N) to the structure of the normal subgroup N and the extention of N to G is discussed. The authors get the following: Theorem 1 Let NG, G/N be a p′-group. Then the prime pφ(1) to arbitrary non-linear irreducible p-Braure character φ∈IBr_p(G｜N) if and only if N has the normal Sylow p-subgroup. Theorem 3 Let G be a p-solvable group, G/N a {p, q}′-group, NG. the prime p≠q, If q｜φ(1) to all non-linear irreducible p-Braure character φ∈IBr_p(G｜N). Then N has a normal q-complement. Theorem 4 Let G be p-solvable group, G/N a p′-group, the subgroup NG. the prime p≠q. If q｜φ(1) to all non-linear irreducible p-Braure character φ∈IBr_p(G｜N′). Then N has a normal q-complement.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第6期929-931,共3页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(10171074).
