# EXPLICIT FREE GROUPS IN DIVISION RINGS

@inproceedings{Gonalves2014EXPLICITFG, title={EXPLICIT FREE GROUPS IN DIVISION RINGS}, author={Jairo Z. Gonçalves and Donald S. Passman}, year={2014} }

- Published 2014
DOI:10.1090/S0002-9939-2014-12230-1

Let D be a division ring of characteristic 6= 2 and suppose that the multiplicative group D• = D \ {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•. The main difficulty occurs here when D has characteristic 0 and the commutators in G are algebraic over Q.