## A combinatorial problem on finite Abelian groups |

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Amsterdam cell-substructure column combinatorial problem completes the proof construct a primitive contain two disjoint contains a zero-structure contains a zero-substructure contains an element contains no zero-substructure contradiction arises create a forbidden cyclic groups disjoint cell-structures disjoint zero-structures disjoint zero-substructures elements taken Emde Boas equivalent formulation Erdos exists a zero-substructure finite Abelian group finite set following implication forbidden element forbidden region four unknown elements given structure group G group is cyclic groups of dimension H.B. Mann implies induction procedure J.E. Olson k+1 elements Kruyswijk length _ length 2n-1 length k+2 Let G linear linear transform Mann and J.E. matrix maximal length Netherlands number of conjunctions P.C. Baayen primitive structure primitive zero-structure Probabilistic methods proof of theorem proper substructure proved the conjecture Report ZW resp restrict ourselves semigroup structure consisting structure of length three unknown elements unit-cell vector zero-structure formed zero-structure of length zero-substructure of length