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

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
Received: 23 January 1974
Published: 1 June 1975
Eric Friedlander
Department of Mathematics
University of Southern California
3620 Vermont Avenue
Los Angeles CA 90089-2532
United States