Full-rank factorings of elementary pp-groups by ZZ-subsets

The paper establishes the existence of a threshold value kpkp for which the following holds. In each factorization of an elementary pp-group of rank less than or equal to kpkp into two ZZ-subsets at least one of the factors does not span the whole group. Further each elementary pp-group of rank greater than kpkp admits factorization into two ZZ-subsets that both span the whole group. Then it will be shown that kp≤11kp≤11 for p≥3p≥3.