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Following the work of B. Kulshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the l-defect of characters of the symmetric group G(n), where l > 1 is an arbitrary integer. We prove that the l-defect is given by an analogue of the hook-length formula, and use it to prove, when n < l(2), an l-version of the McKay conjecture in G(n).
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