The question of whether a subgroup, given by generators, has finite (and then which) index is a natural question in group theory. Unfortunately, for natural groups such as SLn(ℤ) and Sp2n(ℤ), this question cannot have a general algorithmic solution. Nevertheless it is often possible to determine this information in many cases using a computer. I will describe some approaches to this problem and illustrate these in examples.
This is joint work with Alla Detinko (Hull) and Dane Flannery (Galway).
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
