On semigroups defined by Coxeter-type presentations

Colin Matthew Campbell; Edmund Frederick Robertson; Nikola Ruskuc; RM Thomas

doi:10.1017/S0308210500022642

On semigroups defined by Coxeter-type presentations

Colin Matthew Campbell, Edmund Frederick Robertson, Nikola Ruskuc, RM Thomas

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

Abstract

Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.

Original language	English
Pages (from-to)	1063-1075
Number of pages	13
Journal	Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume	125
Issue number	5
DOIs	https://doi.org/10.1017/S0308210500022642
Publication status	Published - Jan 1995

Keywords

ONAN

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10.1017/S0308210500022642

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title = "On semigroups defined by Coxeter-type presentations",

abstract = "Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.",

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author = "Campbell, {Colin Matthew} and Robertson, {Edmund Frederick} and Nikola Ruskuc and RM Thomas",

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AU - Campbell, Colin Matthew

AU - Robertson, Edmund Frederick

AU - Ruskuc, Nikola

AU - Thomas, RM

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N2 - Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.

AB - Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.

KW - ONAN

U2 - 10.1017/S0308210500022642

DO - 10.1017/S0308210500022642

M3 - Article

SN - 0308-2105

VL - 125

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EP - 1075

JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

IS - 5

ER -

On semigroups defined by Coxeter-type presentations

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Keywords

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