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On subnormal subgroups in division rings containing a non-abelian solvable subgroup
- Publication Year :
- 2018
-
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.<br />10 pages
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....8ea11ebd49f17339d5bc1dc488f01813