Explicit free groups in division rings

Gonçalves, J.; Passman, D.

doi:10.1090/S0002-9939-2014-12230-1

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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