Some Properties of Finitely Presented Groups with Topological Viewpoints

TL;DR

This paper uses topological methods involving fundamental groups and covering spaces to provide proofs for key theorems about finitely presented groups, highlighting the interplay between algebraic and topological properties.

Contribution

It offers a topological proof approach for classical theorems on finitely presented groups using properties of fundamental groups and covering spaces.

Findings

Topological proofs for fundamental theorems about finitely presented groups.

Insights into the relationship between algebraic properties and topological structures.

Enhanced understanding of the role of covering spaces in group theory.

Abstract

In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.