Computing with finite semigroups

Friday 5th July, 11:00-12:30, UWS, Parramatta campus, Building EB, Room 1.32

Speaker:

James Mitchell (University of St Andrews)

Title:

COMPUTING WITH FINITE SEMIGROUPS

Abstract:

In this talk I will discuss the problem of how to compute a finite semigroup. What does it mean to `compute' a finite semigroup? It means to find structural information about that semigroup, for example, calculating their Green's classes, size, elements, group of units, minimal ideal, small generating sets, testing membership, finding the inverses of a regular element, factorizing elements over the generators, and so on.

I will review what is known about computing with finite semigroups and give an overview of recently developed functionality in the computer algebra system GAP. No prior knowledge of computing or of semigroup theory will be assumed. Time permitting, I will demonstrate the Semigroups software package for computing with semigroups of transformations and partial permutations, and describe some recent theoretical advances that will allow the methods in Semigroups to be applied to several other natural types of semigroup including monoids of partitions.

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