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
