A Mode of Decomposition for Finite Abelian Groups [antikvár]

I. Geometrical content of the problem for three-dimensional space can be formulated as whether the space can be filled with configurations bodies such as seen in the figure, in a lattice-like shifted arrangement, or not. Or in general, whether the n-dimensional Euclidean space can be filled by the corresponding n-dimensional bodies, the so-called (2,n) semi-crosses in a latticelike arrangement. Since F.KÂRTESZI has set a problem of similar type, several attempts have been published with mosaics of this kind /[l]»[2],[s],[4],[s]/. The same problem has been formulated in a more general method, for semi-crosses (k,n), by S.K.STEIN [s], motivated by the well-known proof by G.HAJÔS deciding over the famous conjecture by H.MINKOWSKI. This paper is centred on the following criterion in algorithmic form: Let the semi-cross (2,n) given.