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We show that the Morita Frobenius number of the blocks of the alternatinggroups, the finite groups of Lie type in describing characteristic, and the Reeand Suzuki groups is 1. We also show that the Morita Frobenius number of almostall of the unipotent blocks of the finite groups of Lie type in non-definingcharacteristic is 1, and that in the remaining cases it is at most 2.

On the Morita Frobenius numbers of blocks of finite reductive groups