From uncountable abelian groups to uncountable nonabelian groups

TL;DR

This paper surveys research on extending abelian group concepts to non-abelian groups, especially focusing on applications to fundamental groups in topology.

Contribution

It introduces generalizations of abelian group theory to non-commutative groups and explores their applications to fundamental groups.

Findings

New generalizations of abelian group notions to non-abelian groups

Applications to understanding fundamental groups in topology

Insights into the structure of uncountable groups

Abstract

The present note surveys my research related to generalizing notions of abelian group theory to non-commutative case and applying them particularly to investigate fundamental groups.