On subnormal subgroups in division rings containing a non-abelian solvable subgroup · arXivDesk1808.09252Aug 28, 201810 pages
On subnormal subgroups in division rings containing a non-abelian solvable subgroup
Bui Xuan Hai, Mai Hoang Bien
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
. In particular, we show that if either
is algebraic over
or
is uncountable, then
contains a non-abelian free subgroup.