Computational group theory

Groups are abstract mathematical objects capturing the concept of symmetry, and therefore are ubiquitous in many mathematical disciplines and other fields of science, such as physics, chemistry, and computer science. This unit is an advanced course on group theory and computational methods, using the computer algebra system GAP. This unit will cover a selection of topics from the following list. Abstract groups: solvable groups, nilpotent groups, groups of prime power order, group extensions and cohomology; Permutation groups: orbit stabiliser algorithm, bases and strong generating sets, membership tests; Group presentations: abelian invariants, Todd-Coxeter algorithm, quotient algorithms; Polycyclic Groups: polycyclic series and generating sets, polycyclic presentations, computing group cohomology; GAP: learn how to use the computer algebra system GAP to compute with groups.