Bounding Fitting Heights of Two Classes of Character Degree Graphs

• 作者: Guangxiang Zhang Xianxiu Zhang
• 来源期刊: 代数集刊:英文版
• 学科: 工学
• 关键词: 曲线拟合 有限可解群 高地 类图 边界 顶点集 证明 字符
• 年，卷（期）: 2014,（2）
• 页码范围: 355-360
• 页数: 6页
• 分类号: TP391.41
• 语种: 中文

摘要

In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ(G) of the character degree graph △(G) of a solvable group G is a disjoint union ρ(G) =π1∪π2, where |πi|≥2 and pi,qi∈πi for i = 1,2, and no vertex in πl is adjacent in △(G) to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.