The typeset and cotypeset of a rank 2 abelian group

Phillip Schultz

Vol. 78 (1978), No. 2, 503–517

DOI: 10.2140/pjm.1978.78.503

Abstract

Let T and T′ be sets of types. This paper describes necessary and sufficient conditions on (T,T′) for the existence of a rank 2 torsion-free abelian group A such that T is the set of types of elements of A, and T′ is the set of types of rank 1 factor groups of A. Moreover, it classifies all such A and gives necessary and sufficient conditions for A to be completely anisotropic.

Mathematical Subject Classification 2000

Primary: 20K15

Milestones

Received: 6 June 1977

Revised: 1 November 1977

Published: 1 October 1978