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