Abstract: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 Haj\'os's factorization theorem.
Keywords: factorization of finite abelian groups, periodic subset, cyclic subset, Haj\'os's theorem
AMS Subject Classification: 20K01 05B45 52C22 68R05