Zappa-Szép products of bands and groups

N. D. Gilbert, S. Wazzan

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Zappa-Szép products arise when an algebraic structure has the property that every element has a unique decomposition as a product of elements from two given substructures. They may also be constructed from actions of two structures on one another, satisfying axioms first formulated by G. Zappa, and have a natural interpretation within automata theory. We study Zappa-Szép products arising from actions of a group and a band, and study the structure of the semigroup that results. When the band is a semilattice, the Zappa-Szép product is orthodox and -unipotent. We relate the construction (via automata theory) to the ?-semidirect product of inverse semigroups devised by Billhardt. © 2008 Springer Science+Business Media, LLC.

Original languageEnglish
Pages (from-to)438-455
Number of pages18
JournalSemigroup Forum
Volume77
Issue number3
DOIs
Publication statusPublished - Dec 2008

Keywords

  • Group
  • Orthodox
  • Semidirect
  • Semigroup
  • Semilattice

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