Conference abstracts

Session S05 - Rings and Algebras

July 28, 16:35 ~ 17:00

## Free groups in a normal subgroup of the field of fractions of a skew polynomial ring

### Jairo Z. Goncalves

### University of Sao Paulo, Brazil - jz.goncalves@usp.br

Let $k(t)$ be the field of rational functions over the field $k$, let $\sigma$ be a $k$-automorphism of $K=k(t)$, let $D=K(X; \sigma)$ be the ring of fractions of the skew polynomial ring $K[X; \sigma]$, and let $D^{\bullet}$ be the multiplicative group of $D$. We show that if $N$ is a non central normal subgroup of $D^{\bullet}$, then $N$ contains a free subgroup.