A presentation for the singular part of the full transformation semigroup

James East

doi:10.1007/s00233-010-9250-1

A presentation for the singular part of the full transformation semigroup

James East

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

14 Citations (Scopus)

Abstract

The (full) transformation semigroup Tn is the semigroup of all functions from the finite set {1, . . . , n} to itself, under the operation of composition. The symmetric group Sn ⊆ Tn is the group of all permutations on {1, . . . , n} and is the group of units of Tn. The complement Tn Sn is a subsemigroup (indeed an ideal) of Tn. In this article we give a presentation, in terms of generators and relations, for Tn Sn, the so-called singular part of Tn.

Original language	English
Pages (from-to)	357-379
Number of pages	23
Journal	Semigroup Forum
Volume	81
Issue number	2
DOIs	https://doi.org/10.1007/s00233-010-9250-1
Publication status	Published - 2010

Keywords

semigroups

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10.1007/s00233-010-9250-1

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abstract = "The (full) transformation semigroup Tn is the semigroup of all functions from the finite set {1, . . . , n} to itself, under the operation of composition. The symmetric group Sn ⊆ Tn is the group of all permutations on {1, . . . , n} and is the group of units of Tn. The complement Tn Sn is a subsemigroup (indeed an ideal) of Tn. In this article we give a presentation, in terms of generators and relations, for Tn Sn, the so-called singular part of Tn.",

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AB - The (full) transformation semigroup Tn is the semigroup of all functions from the finite set {1, . . . , n} to itself, under the operation of composition. The symmetric group Sn ⊆ Tn is the group of all permutations on {1, . . . , n} and is the group of units of Tn. The complement Tn Sn is a subsemigroup (indeed an ideal) of Tn. In this article we give a presentation, in terms of generators and relations, for Tn Sn, the so-called singular part of Tn.

KW - semigroups

UR - http://handle.uws.edu.au:8081/1959.7/550522

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DO - 10.1007/s00233-010-9250-1

M3 - Article

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VL - 81

SP - 357

EP - 379

JO - Semigroup Forum

JF - Semigroup Forum

IS - 2

ER -

A presentation for the singular part of the full transformation semigroup

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