Defining relations for idempotent generators in finite full transformation semigroups

James East

doi:10.1007/s00233-012-9447-6

Defining relations for idempotent generators in finite full transformation semigroups

James East

School of Computer, Data & Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In 1966, John Howie showed that the semigroup $mathcal{T}_{n}setminus mathcal{S}_{n}$ of all singular transformations on a n element set is generated by the set of all idempotent transformations of rank nâˆ’1. We give a presentation for $mathcal{T}_{n}setminus mathcal{S}_{n}$ in terms of this generating set.

Original language	English
Pages (from-to)	451-485
Number of pages	35
Journal	Semigroup Forum
Volume	86
Issue number	3
DOIs	https://doi.org/10.1007/s00233-012-9447-6
Publication status	Published - 2013

Keywords

generators and relations
idempotents
presentations
transformation semigroups

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10.1007/s00233-012-9447-6

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title = "Defining relations for idempotent generators in finite full transformation semigroups",

abstract = "In 1966, John Howie showed that the semigroup $mathcal{T}_{n}setminus mathcal{S}_{n}$ of all singular transformations on a n element set is generated by the set of all idempotent transformations of rank n{\^a}ˆ{\textquoteright}1. We give a presentation for $mathcal{T}_{n}setminus mathcal{S}_{n}$ in terms of this generating set.",

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AB - In 1966, John Howie showed that the semigroup $mathcal{T}_{n}setminus mathcal{S}_{n}$ of all singular transformations on a n element set is generated by the set of all idempotent transformations of rank nâˆ’1. We give a presentation for $mathcal{T}_{n}setminus mathcal{S}_{n}$ in terms of this generating set.

KW - generators and relations

KW - idempotents

KW - presentations

KW - transformation semigroups

UR - http://handle.uws.edu.au:8081/1959.7/521526

U2 - 10.1007/s00233-012-9447-6

DO - 10.1007/s00233-012-9447-6

M3 - Article

SN - 0037-1912

VL - 86

SP - 451

EP - 485

JO - Semigroup Forum

JF - Semigroup Forum

IS - 3

ER -

Defining relations for idempotent generators in finite full transformation semigroups

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