{"paper":{"title":"On defect groups for generalized blocks of the symmetric group","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Jean-Baptiste Gramain","submitted_at":"2007-03-06T15:12:29Z","abstract_excerpt":"In a paper of 2003, B. K\\\"ulshammer, J. B. Olsson and G. R. 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 M. Brou\\'e's conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703157","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}