Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Rajkumar, R.; Devi, P.; Gagarin, Andrei
• Is Part Of: Communications in algebra. Volume 44:Issue 9(2016)
• Page Start: 3705
• Page End: 3726
• Publication Date: 2016-09-01
• Subjects: Finite groups -- Genus -- Nonorientable genus -- Permutability graph -- Projective-planar graph -- Toroidal graph; 05C25 -- 05C10 -- 20E34 -- 57M07; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1087004
• Languages: English
• ISSNs: 0092-7872

Abstract

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.