A Graph Associated with |cd(G)| -1 Degrees of a Solvable Group  

作　　者：Deng Feng LIANG Wu Jie SHI 

机构地区：[1]College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, P. R. China [2]Department of Mathematics, Suzhou University, Jiangsu 215006, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第1期180-182,共3页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10871032);Innovation Project for the Development of Science and Technology (IHLB) (Grant No.201098);the Specific Research Fund of the Doctoral Program of Higher Education of China (Grant No.20060285002)

摘　　要：Let G be a group. We consider the set cd（G）／{m}, where m ∈ cd（G）. We define the graph △（G - m） whose vertex set is p（G - m）, the set of primes dividing degrees in cd（G）／{m}. There is an edge between p and q in p（G - m） ifpq divides a degree a ∈ cd（G）／{m}. We show that if G is solvable, then △（G - m） has at most two connected components.Let G be a group. We consider the set cd（G）／{m}, where m ∈ cd（G）. We define the graph △（G - m） whose vertex set is p（G - m）, the set of primes dividing degrees in cd（G）／{m}. There is an edge between p and q in p（G - m） ifpq divides a degree a ∈ cd（G）／{m}. We show that if G is solvable, then △（G - m） has at most two connected components.

关 键 词：solvable groups irreducible character degrees. 

分 类 号：O152.1[理学—数学] O152.6[理学—基础数学]