Remark on subgroup intersection graph of finite abelian groups - Zhao, Jinxing; Deng, Guixin (Open mathematics (Warsaw, Poland), 2020)
Let be a finite group. The subgroup intersection graph of is a graph whose vertices are non-identity elements of and two distinct vertices and are adjacent if and only if , where is the cyclic subgroup of generated by . In this paper, we show that two finite abelian groups are isomorphic if and only if their subgroup intersection graphs are isomorphic.