特征标维数图是一种连通图的可解群的注记

广西师范大学学报（自然科学版） ›› 2011, Vol. 29 ›› Issue (2): 21-25.

特征标维数图是一种连通图的可解群的注记

梁登峰¹, 于欣言², 秦乐洋²

1.北京工商大学理学院,北京100048;
2.北京工商大学计算机与信息工程学院,北京100048

收稿日期:2011-01-30 发布日期:2018-11-19
通讯作者: 梁登峰(1978—),女,山西平遥人,北京工商大学讲师,博士。E-mail:liangdf@th.btbu.edu.cn
基金资助:
国家自然科学基金资助项目(10871032);北京市属高校科技创新平台项目(201098);教育部博士点基金资助项目(20060285002)

Sovable Groups with Irreducible Character Degrees Graphs Having a Kind of Connected Components

LIANG Deng-feng¹, YU Xin-yan², QIN Le-yang²

1.College of Science,Beijing Technology and Business University,Beijing 100048,China;
2.College of Computer and Information Engineering,Beijing Technology andBusiness University,Beijing 100048,China

Received:2011-01-30 Published:2018-11-19

摘要/Abstract

摘要： 假设群G可解,且特征标维数图Γ(G)的顶点集ρ(G)=π₁∪π₂∪｛p｝,其中|π₁|,|π₂|≥1,π₁∩π₂= ,且π₁与π₂中顶点不相邻。本文证明了G的Fitting高2≤n(G)≤4,且若n(G)≠4,则存在长最多为6的正规子群列G=G₀ G₁ … G_s使商群G_i/G_i+1或者是交换群或者是p-群。

关键词: 有限可解群, 特征标维数图, 导长

Abstract: Let G be solvable,and ρ(G)=π₁∪π₂∪｛p｝ is disjoint union,where |π₁|,|π₂|≥1,π₁∩π₂= .Assume that no prime in π₁ is adjacent in Γ(G) to any prime in π₂.Then the Fitting height 2≤n(G)≤4,and when n(G)≠4,there are G=G₀ G₁ … G_s such that G_i/G_i+1 is either an ablian groupor a p-group,where s≤6.

Key words: finite solvable groups, irreducible character degreesgraphs, derived length

中图分类号:

O152.6

梁登峰, 于欣言, 秦乐洋. 特征标维数图是一种连通图的可解群的注记[J]. 广西师范大学学报（自然科学版）, 2011, 29(2): 21-25.

LIANG Deng-feng, YU Xin-yan, QIN Le-yang. Sovable Groups with Irreducible Character Degrees Graphs Having a Kind of Connected Components[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(2): 21-25.

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