Full-rank factorings of elementaryp-groups byZ-subsets

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