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As a consequence, we show that Donovan's conjecture holds for elementary abelian 2-groups, and that the entries of the Cartan matrices are bounded in terms of the defect for arbitrary abelian 2-groups. We also show that a block with defect groups of the form $C_{2^m} \\times C_{2^m}$ for $m \\geq 2$ has one of two Morita equivalence types and hence is Morita equivalent to the Brauer correspondent block of the normaliser of a defect group. 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