Presentations of inverse semigroups, their kernels and extensions

C.A. Carvalho; R Gray; Nik Ruskuc

doi:10.1017/S1446788711001297

Presentations of inverse semigroups, their kernels and extensions

C.A. Carvalho, R Gray, Nik Ruskuc

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

Abstract

Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.

Original language	English
Pages (from-to)	289-316
Journal	Journal of the Australian Mathematical Society
Volume	90
Issue number	3
DOIs	https://doi.org/10.1017/S1446788711001297
Publication status	Published - 1 Jun 2011

Keywords

Inverse semigroup presentations
Reidemeister-Schreier
Kernel
Finiteness conditions

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10.1017/S1446788711001297

CarvalhoGrayRuskucPresentationsForKernels
This is an author version of the article. The published version copyright (c) Australian Mathematical Publishing Association Inc. 2011 is available from http://journals.cambridge.org
Submitted manuscript, 377 KB

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
Ruskuc, N. (PI) & Quick, M. (CoI)
EPSRC
1/03/10 → 31/05/14
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

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title = "Presentations of inverse semigroups, their kernels and extensions",

abstract = "Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.",

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AU - Carvalho, C.A.

AU - Gray, R

AU - Ruskuc, Nik

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N2 - Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.

AB - Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.

KW - Inverse semigroup presentations

KW - Reidemeister-Schreier

KW - Kernel

KW - Finiteness conditions

U2 - 10.1017/S1446788711001297

DO - 10.1017/S1446788711001297

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SP - 289

EP - 316

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 3

ER -

Presentations of inverse semigroups, their kernels and extensions

Abstract

Keywords

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Projects

Automata Languages Decidability: Automata, Languages, Decidability in Algebra

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

Cite this