摘要
从群的不可约特征标维数的若干信息来推知群的结构一直是群表示论的重要课题 .ManzO在文献 [2～ 6 ]中研究了可解群G的特征标图Γ(G)图论性质 ,并且当Γ(G)不连通时 ,给出了G的纯群理论性质 (引理 1) .本文将讨论若Γ(G)为连通图 ,Γ(G)有怎样的图论性质以及它们如何影响可解群G的结构 ,从而推广了文献 [2～ 6
It is an important topic of group representation theory that group construction is guessed with some informations of group irreducible characterical dimension all the time.Manz O studied graph theory's property of finite soluble group G's character graph Γ(G) in reference [2～6]and provided clean group theoretical property of G (Lemma 1) when Γ(G) is not connected.When Γ(G) is connected graph,this paper discusses what Γ(G) has graph theory's property and how they affect construction of finite soluble group G ,thereby generalizes some results of reference [2～6].
