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Semigroup presentations for test local groups
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| In this paper we exhibit a type of semigroup presentation 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 $κ-identities involving κ-terms of rank at most 1, where κ denotes the implicit signature consisting of the multiplication and the (ω-1)-power. | 393.01 KB | Adobe PDF |
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Abstract(s)
In this paper we exhibit a type of semigroup presentation 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 $κ-identities involving κ-terms of rank at most 1, where κ denotes the implicit signature consisting of the multiplication and the (ω-1)-power.
Description
Keywords
Canonical form Local group Pseudovariety Rees matrix semigroup Semigroup presentation κ-term
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Citation
Costa, J.C., Nogueira, C. & Teixeira, M.L. Semigroup presentations for test local groups. Semigroup Forum 90, 731–752 (2015). https://doi.org/10.1007/s00233-014-9656-2
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Springer Nature
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