On the Capability of Finite Abelian Pairs of Groups

Authors

  • Azam hokmabadi Payame Noor University
  • Marzieh Afkanpoor Ferdowsi University of Mashhad
  • Saeed Kayvanfar Ferdowsi University of Mashhad

Keywords:

Capability, Pairs of groups, Finite abelian 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.

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Published

2015-06-28

Issue

Vol. 9

Section

Vol. 9, No. 2, (2015)

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