Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs. Issue 9 (1st September 2016) - Rajkumar, R.; Devi, P.; Gagarin, Andrei
Abstract : Let G be a group. The permutability graph of subgroups of G, denoted by Γ( G ), is a graph having all the proper subgroups of G as its vertices, and two subgroups are adjacent in Γ( G ) if and only if they permute. In this article, 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 1, 5, P 5, P 6, C 6, or K 3, 3 as a subgraph.