Finite groups whose prime graph on class sizes is a block square

2021/03/31 by Víctor Sotomayor, Sotomayor, Víctor
Chemistry · Mathematics · #20E45 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Synthesis and Characterization of Heterocyclic Compounds #Synthesis and Reactivity of Heterocycles

paper · pdf · doi:10.48550/arxiv.2104.00160

openalex publication_date 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group, and let Δ(G) be the prime graph built on its set of conjugacy class sizes: this is the (simple undirected) graph whose vertices are the prime numbers dividing some conjugacy class size of G, and two distinct vertices p, q are adjacent if and only if pq divides some class size of G. In this paper, we characterise the structure of those groups G whose prime graph Δ(G) is a block square.

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