Graphs associated to conjugacy classes of normal subgroups in finite groups

JOURNAL OF ALGEBRA

卷:443

Article

Beltran, Antonio¹  Jose Felipe, Maria²  Melchor, Carmen³ 

[1] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, E-46022 Valencia, Spain

[3] Univ Jame I, Dept Educ, Castellon de La Plana 12071, Spain

关键词: Finite groups;    Conjugacy classes;    Normal subgroups;    Graphs;   

DOI  :  10.1016/j.jalgebra.2015.06.040

来源: Elsevier

【 摘 要 】

Let G be a finite group and let N be a normal subgroup of G. We attach to N two graphs Gamma(G)(N) and Gamma(G)*(N) related to the conjugacy classes of G contained in N and to the set of primes dividing the sizes of these classes, respectively. These graphs are subgraphs of the ordinary ones associated to the conjugacy classes of G, Gamma(G) and Gamma*(G), which have been widely studied by several authors. We prove that the number of connected components of both graphs is at most 2, we determine the best upper bounds for the diameters and characterize the structure of N when these graphs are disconnected. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free