Using Geometric Group Theory to Find Free Generators of Subgroups of Free Groups

This paper explores how algebraic topology can be used in group theory. More precisely, it describes how the operations known as folding and collapsing on colored directed graphs can be used to find a set of free generators of subgroups of free groups. The technique is illustrated with several examples.

Authors

Institutions

Publication Details

Journal
Mathematical Modeling and Algorithm Application
Published
2025-09-24
DOI
https://doi.org/10.54097/nfaxz289
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Using Geometric Group Theory to Find Free Generators of Subgroups of Free Groups

K. Li
Mathematical Modeling and Algorithm Application
Geometric and Algebraic Topology
article

Using Geometric Group Theory to Find Free Generators of Subgroups of Free Groups

K. Li
article en

Abstract

This paper explores how algebraic topology can be used in group theory. More precisely, it describes how the operations known as folding and collapsing on colored directed graphs can be used to find a set of free generators of subgroups of free groups. The technique is illustrated with several examples.

Mathematical Modeling and Algorithm ApplicationVol. 6(1)
Keystone College (US)
Openalex Percentile: Top 68%
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Using Geometric Group Theory to Find Free Generators of Subgroups of Free Groups — K. Li · Mathematical Modeling and Algorithm Application (2025) | TGRS Research Map | TGRS