Blocks with defect group D_2ⁿ x C_2^m

2011/02/21 by Benjamin Sambale, Sambale, Benjamin
Mathematics · #20C15 #20C20 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C15 #msc:20C20

paper · pdf · doi:10.48550/arxiv.1102.4267

8 pages, shorter proofs, some typos corrected

arxiv created 2011/05/25 · arxiv updated 2011/05/26

Abstract

We determine the numerical invariants of blocks with defect group D_2ⁿ× C_2^m, where D_2ⁿ denotes a dihedral group of order 2ⁿ and C_2^m denotes a cyclic group of order 2^m. This generalizes Brauer's results for m=0. 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.

Related

• Blocks with defect group D_2ⁿ * C_2^m
• 2-Blocks with minimal nonabelian defect groups
• Brauer's Height Zero Conjecture for metacyclic defect groups
• Real characters in blocks
• Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8