Simple groups with m-regular first prime graph component

Year 2016, Volume: 45 Issue: 3, 705 - 716, 01.06.2016

M. Foroudi Ghasemabadi A. Iranmanesh

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

References

• . .