Factoring Abelian Groups, Cliques in Graphs and Covering Sets.

The paper deals with the following problem: If a finite abelian 2-group is a direct product of its subsets of cardinality 4, does it follow that at least one of the factors is periodic? Two results are presented. In the first one, the structures of the group and the subsets are restricted but the size of the the group is not. In the second one, the group and the factors are general but the order of the group is 26. [ABSTRACT FROM AUTHOR]