Isomorphic near-refinements of some direct decompositions of Abelian groups

1983 ◽  
Vol 33 (1) ◽  
pp. 8-12
Author(s):  
S. Yu. Maksimov
Keyword(s):  
Abelian Groups ◽  
Direct Decompositions

A note on rank and direct decompositions of torsion-free Abelian groups

1961 ◽  
Vol 57 (2) ◽  
pp. 230-233 ◽  
Author(s):  
A. L. S. Corner
Keyword(s):  
Abelian Groups ◽  
Free Abelian Groups ◽  
Positive Integers ◽  
Direct Decompositions ◽  
Torsion Free

Fuchs((1), Problem 22) has asked the following question: Given positive integers ri (1 ≤ i ≤ 4) such thatr1 + r2 = r3 + r4, r1 ≠ r3, r1 ≠ r4, do there exist indecomposable torsion-free Abelian groups Gi (1 ≤ i ≤ 4) such that, where Gi is of rank ri (1 ≤ i ≤ 4)?* We shall show in this note that there do always exist groups Gi with the desired properties; in fact, we shall prove the following stronger result

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