Dualities for self-small groups

Authors:
Simion Breaz and Phill Schultz

Journal:
Proc. Amer. Math. Soc. **140** (2012), 69-82

MSC (2010):
Primary 20K21, 20K30, 20K40

DOI:
https://doi.org/10.1090/S0002-9939-2011-10919-5

Published electronically:
May 12, 2011

MathSciNet review:
2833518

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Abstract: We construct a family of dualities on some subcategories of the quasi-category of self-small groups of finite torsion-free rank which cover the class . These dualities extend several of those in the literature. As an application, we show that a group is determined up to quasi-isomorphism by the -algebras and . We also generalize Butler's Theorem to self-small mixed groups of finite torsion-free rank.

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Additional Information

**Simion Breaz**

Affiliation:
Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania

Email:
bodo@math.ubbcluj.ro

**Phill Schultz**

Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Nedlands, 6009, Australia

Email:
schultz@maths.uwa.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-2011-10919-5

Keywords:
Self-small abelian group,
finite rank torsion-free group,
quotient divisible group,
quasi-homomorphism category

Received by editor(s):
March 31, 2010

Received by editor(s) in revised form:
November 8, 2010

Published electronically:
May 12, 2011

Additional Notes:
The first author is supported by the UEFISCSU-CNCSIS, grant ID489

Communicated by:
Birge Huisgen-Zimmermann

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.