Construction and properties of image-inverse quasigroups. II Original Research Article

We give a more general set of necessary and sufficient conditions for a image-quasigroup to be an image-inverse quasigroup than that given in Part I of the paper and show that the constructions given there are special cases of this more general one. We prove the existence of image-inverse quasigroups for every choice of positive integers image, image, image and we discuss the existence of properly defined direct products in more detail. Finally, we show that the left, right and middle image-nuclei of an image-inverse quasigroup are isomorphic, and in the case of a loop, coincide.