# Topics in Algebra: Computational Group Theory (2024S)

Algorithms and techniques for computations in infinite, finitely presented groups.
## Course topics:

- Stallings' folding and related free group algorithms
- Reidemeister-Schreier Algorithm for computing a presentation of a subgroup.
- Todd-Coxeter coset enumeration
- Rewriting systems and the Knuth-Bendix Algorithm
- Finite state automata and Automatic Groups

We will also introduce free software tools to do the above computations, including GAP, SAGE, KBMAG.

Basic group theory and linear algebra are assumed.
## Syllabus

Syllabus
## Lecture notes/Exercises

Lecture notes and Exercises will be posted on the class Moodle page.
## Literature:

- D. B. A. Epstein, D. F. Holt, and S. E. Rees, The use of Knuth-Bendix methods to solve the word problem in automatic groups, J. Symbolic Comput. 12 (1991), no. 4-5, 397-414, Computational group theory, Part 2.
- David B. A. Epstein and Derek F. Holt, Computation in word-hyperbolic groups, Internat. J. Algebra Comput. 11 (2001), no. 4, 467-487.
- Derek F. Holt, Bettina Eick, and Eamonn A. O'Brien, Handbook of computational group theory, Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2005.
- Ilya Kapovich and Alexei Myasnikov, Stallings foldings and subgroups of free groups, J. Algebra 248 (2002), no. 2, 608-668.

Last updated December 21, 2023.

http://www.mat.univie.ac.at/~cashen/Classes/ComputationalGroupTheory.html