Mathematics & Physics 2015, 8(3), 312–319 УДК 512.548+519.179.1 Finite Representation of Classes of Isomorphic Groupoids Maxim N.Nazarov∗ National Research University of Electronic Technology — MIET Bld. 1, Shokin Square, Zelenograd, Moscow, 124498 Russia Received 29.04.2015, received in revised form 11.05.2015, accepted 20.06.2015 We consider an alternative representation of finite groupoids in the form of hypergraphs with three-vertex edges. <...> Automorphism classes of vertices and edges of this hypergraphs are linearly ordered by a natural indexing algorithm based on a maxi-code for three-dimensional adjacency matrix of the hypergraph. <...> With respect of this indexing is constructed a finite set description for the classes of isomorphic groupoids. <...> We will call [D] the class of isomorphic groupoids, if it is composed of all groupoids which are isomorphic to D. This class obviously has infinite number of elements, and, also, the individual groupoids from class [D] are indistinguishable from the algebraic point of view. <...> That in turn leads to the problem of choosing the etalon representative of class [D], when we consider the practical application of groupoids (see for example [1]). <...> It also seems logical that there could be a way to describe the class of isomorphic groupoids with some complete invariant in a similar way it is done with complete invariants in graph theory. <...> Moreover, in the framework of [2] it was shown that for classical graphs one can define a complete invariant, which will be very close to graphs in its properties. <...> If we construct a similar invariant for groupoids, then it can be used in practice as an alternative finite representation for the classes of isomorphic groupoids [D], as well as a tool for choosing the etalon representative in class [D]. <...> We can associate with any arbitrary groupoid D an oriented† hypergraph G = (D,E) by using a rule: xy = z ⇔ (x, y, z) ∈ E. Thus, in this hypergraph G the edges connect only three vertices and the set of edges E is uniquely defined by the operation on groupoid D. As a result, if we generalize the method of construction of complete graph invariant from the article [2] on this oriented hypergraphs with three-vertex edges, then we will in fact transfer this method on any arbitrary <...>