The genus of the subgroup graph of a finite group

Abstract

For a finite group G denote by γ(L(G)) the genus of the subgroup graph of G. We prove that γ(L(G)) tends to infinity as either the rank of G or the number of prime divisors of |G| tends to infinity.

On the number of edges of cyclic subgroup graphs of finite groups

“…Finite groups with planar subgroup graph have been classified by Starr and Turner [14], Bohanon and Reid [3], and Schmidt [13]. Also, the genus of L(G) * has been studied by Lucchini [10].…”