The existence of free non-cyclic subgroups in weakly locally finite division rings

TL;DR

This paper proves that in weakly locally finite division rings, every non-central subnormal subgroup of the multiplicative group contains free non-cyclic subgroups, revealing structural properties of these algebraic objects.

Contribution

It establishes the existence of free non-cyclic subgroups within non-central subnormal subgroups of the multiplicative group in weakly locally finite division rings, a novel structural insight.

Findings

Non-central subnormal subgroups contain free non-cyclic subgroups

Structural properties of multiplicative groups in weakly locally finite division rings

Extension of known subgroup existence results to this class of division rings

Abstract

In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups.