Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65 years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”