Groups whose prime graph on class sizes has a cut vertex

2019/12/20 by Dolfi, Silvio, Pacifici, Emanuele, Sanus, Lucía +1
#20E45 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1912.09743

Abstract

Let G be a finite group, and let Δ(G) be the prime graph built on the set of conjugacy class sizes of G: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of G, two vertices p and q being adjacent if and only if pq divides some conjugacy class size of G. In the present paper, we classify the finite groups G for which Δ(G) has a cut vertex.

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