北京大学学报(自然科学版)

关于指标阶的Huppert问题

张继平   

  1. 北京大学数学科学学院,北京,100871
  • 收稿日期:1997-12-04 出版日期:1998-04-20 发布日期:1998-04-20

On a Problem by Huppert

ZHANG Jiping   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1997-12-04 Online:1998-04-20 Published:1998-04-20

摘要: 对具有4个顶点的指标阶图进行了研究,证明了下述定理:不存在有限可解G,使得G的指标阶图同构于下面的图: ·——·——·——·这一结果解决了Huppert在1990年提出的一个公开问题。该结果和所用方法也为解决著名的指标图半径猜想开辟了道路。

关键词: 有限可解群, 指标阶图, 表示,

Abstract: It is proved that there exists no finite solvable group G with the following as its character degree graph: .____.____.____. . The result solves an important open problem by Huppert and provides more evidence supporting the well-known conjecture which claims that the diameter of the degree graph of any finite solvable group is at most 2.

Key words: finite solvable group, degree graph, representation, module

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