Volume 35 • Number 1 • 2012   • Capability of a Pair of Groups A. Pourmirzaei, A. Hokmabadi and S. Kayvanfar Abstract. A group $G$ is called capable if it is the group of inner automorphisms of some group $E$. Capable pairs are defined in terms of a relative central extension. In this paper, we introduce the precise center for a pair of groups and prove that this subgroup makes a criterion for characterizing the capability of the pair. We also show that our result sharpens the obtained result in this area. A complete classification of finitely generated abelian capable pairs will also be given. 2010 Mathematics Subject Classification: 20E34, 20E36, 20F28. Full text: PDF