Presentations of inverse semigroups, their kernels and extensions
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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.
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 . DOI: 10.1017/S1446788711001297
Journal of the Australian Mathematical Society
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
"Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland"
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