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Zappa–Szép products of bands and groups

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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 ℒ-unipotent. We relate the construction (via automata theory) to the λ-semidirect product of inverse semigroups devised by Billhardt.

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Authors and Affiliations

  1. School of Mathematical and Computer Sciences & The Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    N. D. Gilbert & S. Wazzan

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  1. N. D. Gilbert
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  2. S. Wazzan
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Correspondence to N. D. Gilbert.

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Communicated by László Márki.

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Gilbert, N.D., Wazzan, S. Zappa–Szép products of bands and groups. Semigroup Forum 77, 438–455 (2008). https://doi.org/10.1007/s00233-008-9065-5

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  • DOI: https://doi.org/10.1007/s00233-008-9065-5

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