Vol. 24, No. 1, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 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 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Isomorphism invariants for Abelian groups modulo bounded groups

Ronald J. Ensey

Vol. 24 (1968), No. 1, 71–91
Abstract

Let 𝒜 be the category of Abelian groups, let be the class of bounded Abelian groups, and form the quotient category 𝒜. The principal goal of this paper is a complete set of invariants for direct sums of countable reduced p-groups, such groups 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 there is an integer k 0 such that for all ordinal numbers α and all integers r 0

∑r               r+∑2k
fG(α + k+ j) ≦    fH(α + j)
j=0               j=0

and

∑r               r+∑2k
fB(α + k+ j) ≦    fG(α + j)
j=0               j=0

where fG(β) and f1J(β) denote the β-th Ulm invariants of G and H, respectively. Thus a complete set of 𝒜-isomorphism invariants for such groups is an equivalence class of Ulm invariants, the equivalence relation being given by these two inequalities.

Mathematical Subject Classification
Primary: 20.30
Milestones
Received: 13 December 1966
Published: 1 January 1968
Authors
Ronald J. Ensey