%0 Journal Article
%T Classification of finite groups with toroidal or projective-planar permutability graphs
%A R. Rajkumar
%A P. Devi
%A Andrei Gagarin
%J Mathematics
%D 2015
%I arXiv
%X Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\Gamma(G)$ if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition, we classify the finite groups whose permutability graph does not contain one of $K_{3,3}$, $K_{1,5}$, $C_6$, $P_5$, or $P_6$ as a subgraph.
%U http://arxiv.org/abs/1505.03462v1