Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

R Gray; Nik Ruskuc

doi:10.1112/plms/pdr054

Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

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

Abstract

Let T_n be the full transformation semigroup of all mappings from the set {1, . . . , n} to itself under composition. Let E = E(T_n) denote the set of idempotents of T_n and let e ∈ E be an arbitrary idempotent satisfying |im (e)| = r ≤ n − 2. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group S_r.

Original language	English
Pages (from-to)	997-1018
Number of pages	28
Journal	Proceedings of the London Mathematical Society
Volume	104
Issue number	5
Early online date	24 Jan 2012
DOIs	https://doi.org/10.1112/plms/pdr054
Publication status	Published - May 2012

Access to Document

10.1112/plms/pdr054

IGFullTransformation8
This is an author version of this article. The definitive version is published in Proceedings of the London Mathematical Society, © 2012 London Mathematical Society
Accepted author manuscript, 257 KB
IGFullTransformation8appAccepted author manuscript, 94.1 KB

Theory of Semigroups: Representation theory of Semigroups
Ruskuc, N. (PI)
EPSRC
1/04/12 → 30/09/15
Project: Standard
Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D. (PI)
EPSRC
1/02/08 → 31/01/11
Project: Standard

Cite this

@article{76383dbd5a1c45c3a6703a6e40181963,

title = "Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid",

abstract = "Let Tn be the full transformation semigroup of all mappings from the set {1, . . . , n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying |im (e)| = r ≤ n − 2. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group Sr.",

author = "R Gray and Nik Ruskuc",

year = "2012",

month = may,

doi = "10.1112/plms/pdr054",

language = "English",

volume = "104",

pages = "997--1018",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "LONDON MATH SOC",

number = "5",

}

TY - JOUR

T1 - Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

AU - Gray, R

AU - Ruskuc, Nik

PY - 2012/5

Y1 - 2012/5

N2 - Let Tn be the full transformation semigroup of all mappings from the set {1, . . . , n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying |im (e)| = r ≤ n − 2. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group Sr.

AB - Let Tn be the full transformation semigroup of all mappings from the set {1, . . . , n} to itself under composition. Let E = E(Tn) denote the set of idempotents of Tn and let e ∈ E be an arbitrary idempotent satisfying |im (e)| = r ≤ n − 2. We prove that the maximal subgroup of the free idempotent generated semigroup over E containing e is isomorphic to the symmetric group Sr.

U2 - 10.1112/plms/pdr054

DO - 10.1112/plms/pdr054

M3 - Article

SN - 0024-6115

VL - 104

SP - 997

EP - 1018

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 5

ER -

Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

Abstract

Access to Document

Fingerprint

Projects

Theory of Semigroups: Representation theory of Semigroups

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids

Cite this