On multiplicative subgroups in division rings

TL;DR

This paper explores properties of subgroups within subnormal subgroups of the multiplicative group of division rings, generalizing previous results and providing new insights into their structure.

Contribution

It introduces new results on subgroups of subnormal subgroups in division rings, extending known theorems in the field.

Findings

Generalized previous results on subgroups of division rings

Identified properties of subnormal subgroups in $D^*$

Enhanced understanding of subgroup structures in division rings

Abstract

Let $D$ be a division ring. In this paper, we investigate properties of subgroups of an arbitrary subnormal subgroup of the multiplicative group $D^*$ of $D$. The new obtained results generalize some previous results on subgroups of $D^*$.