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.
@article{arxiv.2104.00160,
title = {Finite groups whose prime graph on class sizes is a block square},
author = {Víctor Sotomayor},
journal= {arXiv preprint arXiv:2104.00160},
year = {2021}
}