Reconstruction theorems for semigroups of functions which contain all transpositions of a set and for clones with the same property

2016/06/21 by Jonah Maissel, Maissel, Jonah, Matatyahu Rubin +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO) #math.LO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1606.06417

arxiv created 2016/06/21 · openalex publication_date 2016/06/21 · arxiv updated 2016/06/22 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28

Abstract

We prove that if S is a set of functions from a set A to itself, S is closed under composition, and S contains all transpositions of A, then the action of S on Acan be recovered from the semigroup consisting of S together with its compositionoperation. We also prove the analogous statement for clones.

Citations

• Automatic Homeomorphicity of Locally Moving Clones

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