2010/12/20 by Benjamin Sambale, Sambale, Benjamin
Mathematics · #11H55 (Secondary) #20C15 #20C20 #20C40 (Primary) #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:11H55 #msc:20C15 #msc:20C20 #msc:20C40
paper · pdf · doi:10.48550/arxiv.1012.4444
26 pages
arxiv created 2010/12/20 · arxiv updated 2010/12/21
We show (among other things) that Brauer's k(B)-conjecture holds for defect groups with are central extensions of metacyclic 2-groups by cyclic groups. The same holds for defect groups which contain a central cyclic subgroup of index at most 9. In particular the k(B)-conjecture holds for 2-blocks of defect at most 4 and 3-blocks of defect at most 3. As a byproduct we obtain the block invariants of 2-blocks with minimal nonmetacyclic defect groups.