Blocks with defect group D_2ⁿ * C_2^m

2011/05/25 by Benjamin Sambale, Sambale, Benjamin
Mathematics · #20C15 #20C20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C15 #msc:20C20

paper · pdf · doi:10.48550/arxiv.1105.4977

10 pages

arxiv created 2011/05/25 · openalex publication_date 2011/05/25 · arxiv updated 2011/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the numerical invariants of blocks with defect group D_2ⁿ * C_2^m = Q_2ⁿ * C_2^m (central product), where n > 2 and m > 1. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally Eaton's conjecture), Brauer's height zero conjecture, the Alperin-McKay conjecture, Alperin's weight conjecture and Robinson's ordinary weight conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case.

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