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Presentations of inverse semigroups, their kernels and extensions

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CarvalhoGrayRuskucPresentationsForKernels.pdf (377.3Kb)
Date
01/06/2011
Author
Carvalho, C.A.
Gray, R
Ruskuc, Nik
Keywords
Inverse semigroup presentations
Reidemeister-Schreier
Kernel
Finiteness conditions
QA Mathematics
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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.
Citation
Carvalho , C A , Gray , R & Ruskuc , N 2011 , ' Presentations of inverse semigroups, their kernels and extensions ' , Journal of the Australian Mathematical Society , vol. 90 , no. 3 , pp. 289-316 . https://doi.org/10.1017/S1446788711001297
Publication
Journal of the Australian Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1017/S1446788711001297
ISSN
1446-7887
Type
Journal article
Rights
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
Description
"Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland"
Collections
  • Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
  • Pure Mathematics Research
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/1998

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

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