  The Zappa-Szep product was developed independently by Guido Zappa and Jeno
Szep as a generalization of the semidirect product: in the Zappa-Szep product,
neither factor is required to be normal. We explore the basic properties of the
product and show that it applies to settings more general than groups. The
product is remarkable in that it requires almost no hypotheses to fuction at
all and is adaptable to a very large number of situations.
