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PRESENTATIONS OF INVERSE SEMIGROUPS, THEIR KERNELS AND EXTENSIONS
Published online by Cambridge University Press: 08 July 2011
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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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
Footnotes
Carvalho was supported by FCT grant SFRH/BPD/26216/2006. Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland. Gray was also partially supported by FCT and FEDER, project POCTI-ISFL-1-143 of the Centro de Álgebra da Universidade de Lisboa, and by the project PTDC/MAT/69514/2006.
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