Nikolaus Conference 2018

Direct products of semigroups are easy to define and imagine. A direct product is defined in terms of its elements, but to compute with a semigroup, we often want to specify the semigroup by a small generating set. For groups and monoids, it is easy to construct a generating set for a direct product from generating sets for the factors, but for semigroups more generally, this problem requires much more effort. Indeed, a direct product of finitely generating semigroups may not even be finitely generated. In this talk I will describe some of the ideas and algorithms that I developed during my PhD for computing “relatively small” generating sets for direct products of arbitrary finite semigroups.