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Title: Presentations of inverse semigroups, their kernels and extensions
Authors: Carvalho, C.A.
Gray, R
Ruskuc, Nik
Keywords: Inverse semigroup presentations
Finiteness conditions
QA Mathematics
Issue Date: 1-Jun-2011
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 . , 10.1017/S1446788711001297
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.
Version: Preprint
Description: "Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland"
Status: Peer reviewed
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
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
University of St Andrews Research
Pure Mathematics Research

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