Heriot-Watt Mathematics Report Series
HWM07-27, 17 Aug 2007
Zappa-Szep products of bands and groups
N D Gilbert and S Wazzan
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, satsifying 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 $\lambda$-semidirect product of inverse semigroups devised by
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