Projectively Invariant Subgroups of Abelian p-Groups

For a projectively invariant subgroup C of a reduced p-group G, a nondecreasing sequence of ordinals and the symbol 8 is constructed in which the kth position, k = 0, 1, 2, ... , is occupied by the minimum of heights in G of all nonzero elements of the subgroup p(k)C[p]. It is proved that if all elements of this sequence are integers, then the subgroup C is fully invariant.