groups and quasi-equivalence

Authors:
H. P. Goeters and W. J. Wickless

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3145-3150

MSC (1991):
Primary 20K15

DOI:
https://doi.org/10.1090/S0002-9939-98-04734-0

MathSciNet review:
1485477

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Abstract | References | Similar Articles | Additional Information

Abstract: A torsion-free abelian group is if every map from a pure subgroup of into lifts to an endomorphism of The class of groups has been extensively studied, resulting in a number of nice characterizations. We obtain some characterizations for the class of homogeneous groups, those homogeneous groups such that, for pure in every has a lifting to a quasi-endomorphism of An irreducible group is if and only if every pure subgroup of each of its strongly indecomposable quasi-summands is strongly indecomposable. A group is if and only if every endomorphism of is an integral multiple of an automorphism. A group has minimal test for quasi-equivalence ( if whenever and are quasi-isomorphic pure subgroups of then and are equivalent via a quasi-automorphism of For homogeneous groups, we show that in almost all cases the and properties coincide.

**[A]**D. Arnold,**Finite Rank Torsion Free Abelian Groups and Rings**, Springer-Verlag LNM**931**(1982). MR**84d:20002****[A-O'B-R]**D. Arnold, B. O'Brien and J. Reid, Quasipure injective and projective torsion-free abelian groups of finite rank, Proceedings of the London Math. Soc.**38 (**1979), 532-44. MR**84f:20060****[R-1]**J. Reid, On the ring of quasi-endomorphisms of a torsion-free group,**Topics in Abelian Groups**, Scott Foresman, 1963, 51-58. MR**30:158****[R-2]**-, Abelian groups cyclic over their endomorphism rings,**Abelian Group Theory**, Springer-Verlag LNM**1006**(1983), 190-203. MR**85e:16053**

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Additional Information

**H. P. Goeters**

Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849

Email:
goetehp@mail.auburn.edu

**W. J. Wickless**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Email:
wjwick@uconnvm.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04734-0

Received by editor(s):
March 21, 1997

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1998
American Mathematical Society