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Springer Verlag, Semigroup Forum, 3(90), p. 731-752

DOI: 10.1007/s00233-014-9656-2

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Semigroup presentations for test local groups

Journal article published in 2014 by José Carlos Costa, Conceição Nogueira, M. Lurdes Teixeira ORCID
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This paper is available in a repository.

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Abstract

In this paper we exhibit a type of semigroup presentations which determines a class of local groups. We show that the finite elements of this class generate the pseudovariety LG of all finite local groups and use them as test-semigroups to prove that LG and S, the pseudovariety of all finite semigroups, verify the same kappa-identities involving kappa-terms of rank at most 1, where kappa denotes the implicit signature consisting of the multiplication and the (omega-1)-power. ; European Regional Development Fund, through the programme COMPETE ; Fundação para a Ciência e a Tecnologia (FCT), under the project PEst-C/MAT/UI0013/2011