Vol. 29, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Primary Abelian groups modulo finite groups

Ronald J. Ensey

Vol. 29 (1969), No. 1, 77–81
Abstract

Let 𝒜 be the category of Abelian groups, the Serre class of finite Abelian groups, and form the quotient category 𝒜. The purpose of this paper is to find a complete set of invariants for direct sums of countable reduced p-groups, such groups being considered as objects of the category 𝒜. Specifically, it will be shown that two direct sums of countable reduced p-groups G and H are isomorphic in 𝒜if and only if

fG(α) = fH(α) for almost all ordinal numbers α,

and

fG(α) ⁄= fH(α) implies max (fG (α ),fH (α )) < ℵ0.

Mathematical Subject Classification
Primary: 20.30
Milestones
Received: 8 January 1968
Published: 1 April 1969
Authors
Ronald J. Ensey