Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
Full-text PDF Free Access

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 $\mathbb {Q}$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16K40, 20C07

Retrieve articles in all journals with MSC (2010): 16K40, 20C07


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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.