The semidirect product of two groups is a natural generalization of the direct product of two groups in that the requirement that both factors be normal in the product is replaced by the weaker requirement that only one of the factors be normal in the product. The Zappa-Szép product of two groups is a natural generalization of the semidirect product of two groups in that neither factor is requi...

The Alon-Tarsi conjecture states that for even n, the number of even latin squares of order n differs from the number of odd latin squares of order n. Zappa [6] found a generalization of this conjecture which makes sense for odd orders. In this note we prove this extended Alon-Tarsi conjecture for prime orders p. By results of Drisko [2] and Zappa [6], this implies that both conjectures are tru...

We characterise in terms of Zappa-Szép products a class of semigroups which arise from actions of groupoids on semigroups constructed from subshifts of graphs.

The Alon-Tarsi conjecture states that for even n, the number of even latin squares of order n diiers from the number of odd latin squares of order n. Zappa 6] found a generalization of this conjecture which makes sense for odd orders. In this note we prove this extended Alon-Tarsi conjecture for prime orders p. By results of Drisko 2] and Zappa 6], this implies that both conjectures are true fo...