Remark on subgroup intersection graph of finite abelian groups

Jinxing Zhao, Guixin Deng
2020 Open Mathematics  
Let G be a finite group. The subgroup intersection graph \text{Γ}(G) of G is a graph whose vertices are non-identity elements of G and two distinct vertices x and y are adjacent if and only if |\langle x\rangle \cap \langle y\rangle |\gt 1 , where \langle x\rangle is the cyclic subgroup of G generated by x. In this paper, we show that two finite abelian groups are isomorphic if and only if their subgroup intersection graphs are isomorphic.
doi:10.1515/math-2020-0066 fatcat:tojl73ldezfn7avvs42ecgneyq