Zappa–Szép products of bands and groups |
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Authors: | N D Gilbert S Wazzan |
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Institution: | (1) School of Mathematical and Computer Sciences & The Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK |
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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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Keywords: | Semigroup Group Semilattice Orthodox Semidirect |
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