Can I read On Free Subgroups in Division Rings on EtoBox?

On Free Subgroups in Division Rings by Bell, Jason P.; Goncalves, Jairo is a scholarly article available to read on EtoBox.

What is On Free Subgroups in Division Rings about?

Let $K$ be a field and let $\sigma$ be an automorphism and let $\delta$ be a $\sigma$-derivation of $K$. Then we show that the multiplicative group of nonzero elements of the division ring $D=K(x;\sigma,\delta)$ contains a free non-cyclic subgroup unless $D$ is commutative, answering a special case of a conjecture of Lichtman. As an application, we show that division algebras formed by taking the Goldie ring of quotients of group algebras of torsion-free non-abelian solvable-by-finite groups always contain free non-cyclic subgroups.

Author

Bell, Jason P.; Goncalves, Jairo

Published

2018

Language

EN