Mai Hoang Bien, Bui Xuan Hai: On subnormal subgroups in division rings containing
a non-abelian solvable subgroup, 151-162

Abstract:

Let $D$ be a division ring with center $F$ and $N$ a subnormal subgroup of the multiplicative group $D^*$ of $D$. Assume that $N$ contains a non-abelian solvable subgroup. In this paper, we study the problem on the existence of non-abelian free subgroups in $N$. We show that if either $N$ is algebraic over $F$ or $F$ is uncountable, then $N$ contains a non-abelian free subgroup.

Key Words: Subnormal subgroups, free subgroup, solvable subgroup, division ring, quotient division ring.

2010 Mathematics Subject Classification: Primary 16K20, 20E05;
Secondary 16S85, 16S36.