Extension functions for rank 2, torsion free abelian groups

Eric Friedlander

Vol. 58 (1975), No. 2, 371–380

DOI: 10.2140/pjm.1975.58.371

Abstract

The set of isomorphism classes of rank 2, torsion free abelian groups with a pure subgroup isomorphic to a given rank 1 group is shown to be in natural 1-1 correspondence with the set of pairs consisting of a quotient type and a type of an extension function. In terms of these invariants, necessary and sufficient conditions are determined for such a group to be homogeneous or to admit a pure cyclic subgroup. Moreover, this 1-1 correspondence has an explicit inverse, so that examples are readily obtained.

Mathematical Subject Classification 2000

Primary: 20K15

Milestones

Received: 23 January 1974

Published: 1 June 1975