Connectivity of intersection graphs of finite groups


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Kayacan S.

COMMUNICATIONS IN ALGEBRA, vol.46, no.4, pp.1492-1505, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2017.1347662
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.1492-1505

Abstract

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H boolean AND K not equal 1 where 1 denotes the trivial subgroup of G. In this paper, we classify finite solvable groups whose intersection graphs are not 2-connected and finite nilpotent groups whose intersection graphs are not 3-connected. Our methods are elementary.