5-边形块图不能作为有限可解群的特征标素因子图  

Block pentagons cannot occur as character degree graphs of finite solvable groups

作　　者：孟庆云[1] 杜妮[2] MENG Qingyun;DU Ni(School of Sciences,Henan University of Technology,Zhengzhou 450001,China;School of Mathematical Science,Xiamen University,Xiamen 361005,China)

机构地区：[1]河南工业大学理学院,河南郑州450001 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2020年第1期82-84,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11601121,11771356);福建省自然科学基金(2019J01025)

摘　　要：Lewis证明了5-边形不能成为有限可解群的特征标素因子图.本文定义了5-边形块图,并证明了该类图也不能成为有限可解群的特征标素因子图,推广了Lewis的结果.Lewis has proved that pentagons cannot occur as character degree graphs of any finite solvable groups.In this short paper,we generalize the definition of a pentagon graph to graphs that are block pentagons.We investigate character degree graphs of finite solvable groups and show that block pentagons cannot occur as character degree graphs of any solvable groups,either.This discovery generalized Lewis result.

关 键 词：有限可解群 特征标素因子图 5-边形 

分 类 号：O152[理学—数学]