A combinatorial theorem for a symmetric triangulation of the sphere
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.
This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [Invent. Math.44 (1978) 259–264] and the conjecture that the problem is undecidable.