SUBGROUP INTERSECTION GRAPH OF FINITE ABELIAN GROUPS

Abstract. let g be a finite group with the identity e. the subgroup intersection graph ??si (g) of gis the graph with vertex set v (??si (g)) = g??e and two distinct vertices x and y are adjacent in ??si (g)if and only if j hxi hyi j > 1, where hxi is the cyclic subgroup of g generated by x 2 g. in this paper,we obtain a lower bound for the independence number of subgroup intersection graph. we characterizecertain classes of subgroup intersection graphs corresponding to finite abelian groups. finally, wecharacterize groups whose automorphism group is the same as that of its subgroup intersection graph.