On the Number of Irreducible Characters in a 3-block with a Minimal Nonabelian Defect Group

作     者：Sheng YANG Sheng GAO Chong Bin XU 

作者机构：Department of Mathematics Wenzhou University Department of Mathematics Hefei University of Technology 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2017年第33卷第9期

页      面：1267-1274页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.13101193) Zhejiang Natural Science Foundation(Grant No.LY16A010016) 

主　　题：Characters blocks defect groups inertial groups 

摘      要：Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs＇ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k（B） and a set of irreducible Brauer characters of G having cardinality l（B）. We calculate k（B） and l（B） provided that D is normal in G and D = （x, y, z｜x3n=y3m = z3 = [x, z] = [y, z] = 1, [x, y] = z） （n 〉 m 〉 2）.