Group theory via global semigroup theory

Combinatorial Group Theory, Inverse Monoids, Automata, And Global Semigroup Theory

Combinatorial Group Theory , Inversemonoids , Automata , and Global Semigroup

Geometric Semigroup Theory

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...

Syntactic and Global Semigroup Theory, a Synthesis Approach

This paper is the culmination of a series of work integrating syntactic and global semigroup theoretical approaches for the purpose of calculating semidirect products of pseudovarieties of semigroups. We introduce various abstract and algorithmic properties that a pseudovariety of semi-groups might possibly satisfy. The main theorem states that given a nite collection of pseudovarieties, each s...

Profinite Methods in Semigroup Theory

A highlight of the Conference held at the University of Nebraska-Lincoln in May 2000 was the proof of the decidability of the complexity of nite semigroups and automata, presented by Rhodes 78]. This problem had been open for more than thirty years and had inspired many active branches of semigroup theory. As is usually the case with old and diicult problems, the solution for the original quest...