On the Capability of Finite Abelian Pairs of Groups

Abstract

A group $G$ is called capable if it is isomorphic to the group of inner automorphisms of some group $H$. The notion of capable groups was extended to capable pairs by G. Ellis, in 1996. Recently, a classification of capable pairs of finite abelian groups was given by A. Pourmirzaei, A. Hokmabadi and S. Kavanfar. In this paper, we give a different characterization of capable pairs of finite abelian groups in terms of a condition on the lattice of subgroups.