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Abstract
Several problems about generalizations of the Davenport constant in abelian and non-abelian finite groups are considered here. Relations among these generalizations are established and some partial solutions are provided. New bounds are given for the Davenport constant for groups of rank three of type: Z n⊗ Z nm⊗ Z nmq for n=2,3, as an application of the partial solutions to the proposed problems.
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