MT538 Representations of Groups

Information

Course Goal

Study Proportions of some elamantary groups and some free grop constructions

Course Content

Basic definitions, Group Effects, Group Presentations, Semigroup Presentations, Abelyen Group Presentations, Representation Theory, Modules, Object Theory Computer Representation of Groups, Use of Random Methods in Computable Groups, Calculations with Homomorphisms, Computation of Orbit and Stabilizers, Schreier Vectors, Block System Discovery, Basis and Generators Clusters Simple methods, Koset calculation strategies, Subgroup presentations, Group presentations for the cosmetics table Finding the presentation of a group, Todd-Coxeter-Schreier-Sims Algorithm Calculations in finite fields, Cohomology, Character Table Calculation, Polycyclic Presentations, Polycyclic group examples, Factor groups and homomorphisms Finite and finite automorphism groups, some useful subgroups, calculation compositions and Chief Series, Solable radical method applications, Monoid Presentations, Rewriting Systems, Monoid and rewriting systems in groups. Finite otomoto, Finite automate operations, Automatic groups

Course Precondition

Yok

Resources

Group Representations J.L. Alperin Rowen B. Bell

Notes

Lecture Notes

Course Learning Outcomes

Relation with Program Learning Outcome

Week Plan

Student Workload - ECTS