Vol. 58, No. 2, 1975

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Extension functions for rank 2, torsion free abelian groups

Eric Friedlander

Vol. 58 (1975), No. 2, 371–380
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
Authors
Eric Friedlander
Department of Mathematics
University of Southern California
3620 Vermont Avenue
Los Angeles CA 90089-2532
United States