Multiplicative Subgroups in weakly locally finite division rings

TL;DR

This paper investigates the subgroup structure of weakly locally finite division rings, a broad class extending locally finite division rings, contributing to the understanding of non-commutative division ring theory.

Contribution

It provides new insights into the subgroup structure of weakly locally finite division rings, expanding the understanding beyond locally finite division rings.

Findings

Characterization of subgroup structures in weakly locally finite division rings

Extension of known results from locally finite to weakly locally finite division rings

Advancement in the theory of skew linear groups

Abstract

The description of the subgroup structure of a non-commutative division ring is the subject of the intensive study in the theory of division rings in particular, and of the theory of skew linear groups in general. This study is still so far to be complete. In this paper, we study this problem for weakly locally finite division rings. Such division rings constitute a large class which strictly contains the class of locally finite division rings.