Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles  

作　　者：Huan Xiong 

机构地区：[1]Institut fur Mathematik, Universitat Zurich, Winterthurerstrasse 190 CH-8057 Zurich, Switzerland

出　　处：《Algebra Colloquium》2016年第1期15-22,共8页代数集刊（英文版）

摘　　要：Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.

关 键 词：finite group character graph codegree 

分 类 号：O152.1[理学—数学] TP391.41[理学—基础数学]