Regularity on Near Permutation Semigroups

Abstract

A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group of permutations on N elements and by a set of transformations of rank N − 1. The aim of this paper is to determine computationally efficient conditions to test whether or not a near permutation semigroup is regular.

Key Words:

• Transformation semigroups
• Near permutation semigroups
• Regular semigroups

Mathematics Subject Classification:

• Primary 20M20
• Secondary 20M17

Acknowledgment

The author acknowledges the financial support of the Sub-Programa Cieˆncia e Tecnologia do 2^o Quadro Comunitário de Apoio (grant number BD/18012/98) and project POCTI/32440/MAT/2000 (CAUL) of FCT and FEDER.

Notes

^#Communicated by P. Higgins.