On subnormal subgroups in division rings containing a non-abelian solvable subgroup

Bui Xuan Hai; Mai Hoang Bien

On subnormal subgroups in division rings containing a non-abelian solvable subgroup

Rings and Algebras 2018-08-29 v1 Group Theory

Authors: 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 $N$ . In particular, we show that if either $N$ is algebraic over $F$ or $F$ is uncountable, then $N$ contains a non-abelian free subgroup.

Keywords

abelian groups

Cite

@article{arxiv.1808.09252,
  title  = {On subnormal subgroups in division rings containing a non-abelian solvable subgroup},
  author = {Bui Xuan Hai and Mai Hoang Bien},
  journal= {arXiv preprint arXiv:1808.09252},
  year   = {2018}
}

Comments

10 pages

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