Vol. 45, No. 2, 1973

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The constructive theory of countable abelian p-groups

Fred Richman

Vol. 45 (1973), No. 2, 621–637
Abstract

The purpose of this paper is to develop the theory of abelian p-groups along constructive lines. To this end a constructive theory of ordinal numbers and an axiomatic treatment of the notion of height are presented. The classical theorems of Zippin and Ulm concerning existence and uniqueness of countable p-groups with prescribed invariants are proved in a finitistic setting.

Mathematical Subject Classification 2000
Primary: 02E05
Secondary: 20E15
Milestones
Received: 2 December 1971
Revised: 18 January 1973
Published: 1 April 1973
Authors
Fred Richman