On the prime graph of simple groups

Burness, Timothy C.; Covato, Elisa

Abstract

Let G be a finite group, let π(G) be the set of prime divisors of jGj and let Γ(G) be the prime graph of G. This graph has vertex set π(G), and two vertices r and s are adjacent if and only if G contains an element of order rs. Many properties of these graphs have been studied in recent years, with a particular focus on the prime graphs of finite simple groups. In this note, we determine the pairs (G; H), where G is simple and H is a proper subgroup of G such that Γ(G) = Γ(H).

• Journal Article Type: Article
• Online Publication Date: Oct 8, 2014
• Publication Date: Apr 26, 2015
• Deposit Date: Apr 25, 2024
• Journal: Bulletin of the Australian Mathematical Society
• Print ISSN: 0004-9727
• Electronic ISSN: 1755-1633
• Publisher: Cambridge University Press (CUP)
• Peer Reviewed: Peer Reviewed
• Volume: 91
• Issue: 2
• Pages: 227-240
• DOI: https://doi.org/10.1017/S0004972714000707
• Public URL: https://uwe-repository.worktribe.com/output/11915345