On sufficient conditions for being finite quandles

In 2006, Nelson and Wong introduced that every finite quandle can be decomposed into a disjoint union of some quandles and for given n quandles satisfying certain conditions, there is a quandle which is a disjoint union of the n quandles. In 2008, Ehrman, Gurpinar, Thibault and Yetter also introduced similar results about the decomposition of quandles. In this paper, we observe an operation table Q which consists of four sub-operation tables, where diagonal tables are quandle operations. We study which conditions make Q a quandle operation table.