Finite state wreath powers of transformation semigroups.
type: Item
instance of: scholarly article
title: Finite state wreath powers of transformation semigroups.
zbMATH Open document ID: 1229.20069
author: Juan-Miguel Gracia
published in: Semigroup Forum
publication date: 2011-09-06T00:00:00Z
review text: The author introduces the notion of a finite state wreath power \(FW^\infty(T,X)\) of a given transformation semigroup \((T,X)\) as a naturally defined subsemigroup in the projective limit of the finite wreath powers of \((T,X)\). The author establishes a criterion for semitransitivity of the wreath product of transformation semigroups and shows that \(FW^\infty(T,X)\) acts transitively on the set of ultimately periodic infinite words over \(X\) provided that \((T,X)\) is transitive. Further, the author shows that the finite state wreath power of a nontrivial transformation semigroup is not finitely generated. Finally, it is shown that the finite state wreath power of a finite transformation monoid containing a non-injective transformation does not contain irreducible generating systems.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 5945592
zbMATH Keywords: wreath products
zbMATH Keywords: finite state wreath powers
zbMATH Keywords: transformation semigroups
zbMATH Keywords: actions
zbMATH Keywords: generating systems
zbMATH Keywords: free products
MaRDI profile type: Publication
full work available at URL: s00233-011-9292-z
OpenAlex ID: W2065346793
cites work: Q4079524
cites work: Q5302760
cites work: Algebraic Theory of Automata Networks
cites work: Semitransitive subsemigroups of the symmetric inverse semigroups.
DOI: 10.1007/S00233-011-9292-Z
description: scientific article; zbMATH DE number 5945592