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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Explicit free groups in division rings
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by J. Z. Gonçalves and D. S. Passman PDF
Proc. Amer. Math. Soc. 143 (2015), 459-468 Request permission

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
  • MR Author ID: 75040
  • Email: jz.goncalves@usp.br
  • D. S. Passman
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 136635
  • Email: passman@math.wisc.edu
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 3283636