Bulletin of the Australian Mathematical Society

Research Article

ON GENERATORS AND PRESENTATIONS OF SEMIDIRECT PRODUCTS IN INVERSE SEMIGROUPS

E. R. DOMBIa1 and N. RUŠKUCa2 c1

a1 School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK (email: erzsi@mcs.st-and.ac.uk)

a2 School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK (email: nik@mcs.st-and.ac.uk)

Abstract

In this paper we prove two main results. The first is a necessary and sufficient condition for a semidirect product of a semilattice by a group to be finitely generated. The second result is a necessary and sufficient condition for such a semidirect product to be finitely presented.

(Received March 06 2008)

2000 Mathematics subject classification

  • primary 20M05; secondary 20M18;
  • 20M30

Keywords and phrases

  • inverse semigroups;
  • semidirect products;
  • generators;
  • presentations;
  • groups;
  • semilattices;
  • actions

Correspondence:

c1 For correspondence; e-mail: nik@mcs.st-and.ac.uk