Author/Authors :
Pourmirzaei, A. ferdowsi university of mashhad - Center of Excellence in Analysison Algebraic Structures - Department of Pure Mathematics, مشهد, ايران , Hokmabadi, A. ferdowsi university of mashhad - Center of Excellence in Analysison Algebraic Structures - Department of Pure Mathematics, مشهد, ايران , Kayvanfar, S. ferdowsi university of mashhad - Center of Excellence in Analysison Algebraic Structures - Department of Pure Mathematics, مشهد, ايران
Abstract :
A group G is called capable if it is the group of inner automorphisms of some group E. Capable pairs are dened 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 classication of finitely generated abelian capable pairs will also be given.
