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Journal of the London Mathematical Society Advance Access originally published online on April 25, 2008
Journal of the London Mathematical Society 2008 78(1):155-171; doi:10.1112/jlms/jdn023
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© 2008 London Mathematical Society

On defect groups for generalized blocks of the symmetric group

Jean-Baptiste Gramain

École Polytechnique Fédérale de Lausanne
IGAT
Bâtiment de Chimie(BCH)
CH-1015 Lausanne
Switzerland

In a paper of 2003, Külshammer, Olsson and Robinson defined {ell}-blocks for the symmetric groups, where {ell}>1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal {ell}-block. We then check that, in the Abelian case, we have an analogue of one of Broué's conjectures.

2000 Mathematics Subject Classification 20C30 (primary), 20C15, 20C20 (secondary).

Received March 8, 2007; revised February 15, 2008; published online April 25, 2008.


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