Factoring a finite Abelian group by prime complexes.
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
A set Q is a faithful homogeneous space over a commutative group iff there is a family S of mappings such that (Q,S) is a TST-space.