Bounding Fitting Heights of Two Classes of Character Degree Graphs

作     者：Xianxiu Zhang Guangxiang Zhang 

作者机构：School of Electronic and Information Engineering Southwest University Chongqinng 400715 China Department of Mathematics Liupanshui Normal University Liupanshui Guizhou 553001 China School of Mathematics and Statistics Southwest University Chongqing 400715 China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2014年第21卷第2期

页      面：355-360页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 0802[工学-机械工程] 0701[理学-数学] 

基　　金：Supported by the Research Fund of Liupanshui Normal University the Fund of Guizhou Educational Research 

主　　题：Fitting height character degree graph solvable group 

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.