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

Authors

  • Kewei Li

DOI:

https://doi.org/10.54097/nfaxz289

Keywords:

Geometric Group Theory, Free Group, Subgroup, Free Generator, Graph Folding, Graph Collapsing

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.

References

[1] W. R. Scott, Group Theory, Courier Corporation, 2012.

[2] M. Hall, The Theory of Groups, Courier Dover Publications, 2018.

[3] M. Clay and D. Margalit, Office Hours with a Geometric Group Theorist, Princeton University Press, 2017.

[4] J. J. Rotman, An Introduction to Algebraic Topology, Springer Science & Business Media, 2013.

[5] N. Biggs, E. K. Lloyd and R. J. Wilson, Graph Theory, 1736-1936, Oxford University Press, 1986.

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Published

24-09-2025

Issue

Vol. 6 No. 1 (2025)

Section

Articles

License

Copyright (c) 2025 Kewei Li

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Li, K. (2025). Using Geometric Group Theory to Find Free Generators of Subgroups of Free Groups. Mathematical Modeling and Algorithm Application, 6(1), 1-6. https://doi.org/10.54097/nfaxz289