PRODUCTS OF LACUNARY SUBSETS OF A FINITE ABELIAN

GROUP by Sándor Szabó, Isa Town, State of Bahrain

Abstract. Hajós’ theorem asserts that if a finite abelian group is a direct product of cyclic subsets, then in fact at least one of the factors must be a subgroup. A cyclic subset is the “front section” of a cyclic subgroup. The paper generalizes the result proving that the same conclusion holds if the factors are consisting of “not connected sections” of a cyclic subgroup provided the number of these sections is “relatively small”. Mathematics subject classification: 20K01, 52C22 Keywords: Factoring finite abelian groups by subsets, Hajós-Rédei theory.