38 research outputs found

    The Isaacs-Navarro Conjecture for covering groups of the symmetric and alternating groups in odd characteristic

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    In this paper, we prove that a refinement of the Alperin-McKay Conjecture for pp-blocks of finite groups, formulated by I. M. Isaacs and G. Navarro in 2002, holds for all covering groups of the symmetric and alternating groups, whenever pp is an odd prime

    On defect groups for generalized blocks of the symmetric group

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    In a paper of 2003, B. K\"ulshammer, J. B. Olsson and G. R. Robinson defined ℓ\ell-blocks for the symmetric groups, where ℓ>1\ell >1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal ℓ\ell-block. We then check that, in the Abelian case, we have an analogue of one of M. Brou\'e's conjectures.Comment: 18 page

    Defect of characters of the symmetric group

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