Mahlo cardinals and the torsion product of primary abelian groups

Patrick W. Keef

Vol. 259 (2012), No. 1, 117–139

DOI: 10.2140/pjm.2012.259.117

Abstract

Nunke’s problem asks when the torsion product of two abelian p-groups is isomorphic to a direct sum of cyclic groups. A complete solution to the problem is given using a new invariant, denoted by L_G, whose values are certain collections of finite sets of uncountable regular cardinals. This is a refinement of a previous approach to the problem that only worked up to the first cardinal that is weakly Mahlo. The multiplicative properties of L_G are then related to the generalized continuum hypothesis.

Keywords

primary abelian group, Mahlo cardinals, torsion product

Mathematical Subject Classification 2010

Primary: 20K10, 20K40

Milestones

Received: 13 December 2011

Accepted: 17 April 2012

Published: 31 August 2012