Automatic semigroup acts

Erzsébet R. Dombi, Miklós Hartmann

Research output: Contribution to journalArticle

Abstract

To give a general framework for the theory of automatic groups and semigroups, we introduce the notion of automaticity for semigroup acts. We investigate their basic properties and discuss how the property of being automatic behaves under changing the generators of the acting semigroup and under changing the generators of the semigroup act. In particular, we prove that under some conditions on the acting semigroup, the automaticity of the act is invariant under changing the generators. Since automatic semigroups can be seen as a special case of automatic semigroup acts, our result generalizes and extends the corresponding result on automatic semigroups, where the semigroup S satisfies S=SSS=SS. We also give a geometric approach in terms of the fellow traveller property and discuss the solvability of the equality problem in automatic semigroup acts. Our notion gives rise to a variety of definitions of automaticity depending on the set chosen as a semigroup act and we discuss future research directions.
LanguageEnglish
Pages286–307
Number of pages22
JournalJournal of Algebra
Volume435
Early online date20 Apr 2015
DOIs
Publication statusPublished - 1 Aug 2015

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Semigroup
Generator
Geometric Approach
Solvability
Equality
Generalise
Invariant

Keywords

  • semigroup acts
  • automaticity
  • change of generators

Cite this

Dombi, Erzsébet R. ; Hartmann, Miklós. / Automatic semigroup acts. In: Journal of Algebra. 2015 ; Vol. 435. pp. 286–307.
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Automatic semigroup acts. / Dombi, Erzsébet R.; Hartmann, Miklós.

In: Journal of Algebra, Vol. 435, 01.08.2015, p. 286–307.

Research output: Contribution to journalArticle

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