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Explicit free groups in division rings


Authors: J. Z. Gonçalves and D. S. Passman
Journal: Proc. Amer. Math. Soc. 143 (2015), 459-468
MSC (2010): Primary 16K40; Secondary 20C07
DOI: https://doi.org/10.1090/S0002-9939-2014-12230-1
Published electronically: October 1, 2014
MathSciNet review: 3283636
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ D$ be a division ring of characteristic $ \neq 2$ and suppose that the multiplicative group $ D^\bullet =D\setminus \{0\}$ has a subgroup $ G$ isomorphic to the Heisenberg group. Then we use the generators of $ G$ to construct an explicit noncyclic free subgroup of $ D^\bullet $. The main difficulty occurs here when $ D$ has characteristic 0 and the commutators in $ G$ are algebraic over $ \mathbb{Q}$.


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Additional Information

J. Z. Gonçalves
Affiliation: Department of Mathematics, University of São Paulo, São Paulo, 05508-090, Brazil
Email: jz.goncalves@usp.br

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12230-1
Received by editor(s): February 27, 2013
Published electronically: October 1, 2014
Additional Notes: The first author’s research was supported in part by Grant CNPq 300.128/2008-8 and by Fapesp-Brazil, Proj. Tematico 2009/52665-0
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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