- Hacettepe Journal of Mathematics and Statistics
- Vol: 45 Issue: 3
- Simple groups with m-regular first prime graph component
Simple groups with m-regular first prime graph component
Authors : M. Foroudi Ghasemabadi, A. Iranmanesh
Pages : 705-716
View : 14 | Download : 6
Publication Date : 2016-06-01
Article Type : Research
Abstract :Let G be a finite simple group and GK(G) be the prime graph of G. The connected component of GK(G) whose vertex set contains 2 is denoted by $\pi_1(G)$. In this paper, our purpose is to classify the finite simple groups G such that $\pi_1(G)$ is regular. We prove that $\pi_1(G)$ is regular if and only if all the connected components of GK(G) are cliques.Keywords : Prime graph, simple groups, regular graph