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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quotient divisible abelian groups


Authors: A. Fomin and W. Wickless
Journal: Proc. Amer. Math. Soc. 126 (1998), 45-52
MSC (1991): Primary 20K21, 20K40
DOI: https://doi.org/10.1090/S0002-9939-98-04230-0
MathSciNet review: 1443826
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Abstract: An abelian group $G$ is called quotient divisible if $G$ is of finite torsion-free rank and there exists a free subgroup $F\subset G$ such that $G/F$ is divisible. The class of quotient divisible groups contains the torsion-free finite rank quotient divisible groups introduced by Beaumont and Pierce and essentially contains the class $\mathcal{G}$ of self-small mixed groups which has recently been investigated by several authors. We construct a duality from the category of quotient divisible groups and quasi-homomorphisms to the category of torsion-free finite rank groups and quasi-homomorphisms. Our duality when restricted to torsion-free quotient divisible groups coincides with the duality of Arnold and when restricted to $\mathcal{G}$ coincides with the duality previously constructed by the authors.


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Additional Information

A. Fomin
Affiliation: Algebra Department, Moscow State Pedagogical University, Moscow, Russia
Email: fomin.algebra@mpgu.msk.su

W. Wickless
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: wjwick@uconnvm.uconn.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04230-0
Received by editor(s): June 14, 1996
Dedicated: Dedicated to the memory of Ross A. Beaumont
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society