arXiv subjects

Benjamin Sambale

Publications and source records attributed to Benjamin Sambale.

75 records · Page 5Linked to original sources

arXiv2010

Cartan matrices and Brauer's k(B)-conjecture

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.

math.RT↗

arXiv2010

2-Blocks with minimal nonabelian defect groups

We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by Rédei. If the defect group is also metacyclic, then the block invariants are known. In the remaining cases there are only two (infinite) families of "interesting" defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and the Olsson-conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture is satisfied. This paper is a part of the author's PhD thesis.

math.RT↗

arXiv2010

Fusion systems on metacyclic 2-groups

Let P be a finite metacyclic 2-group and F a fusion system on P. We prove that F is nilpotent unless P has maximal class or P is homocyclic, i.e. P is a direct product of two isomorphic cyclic groups. As a consequence we obtain the numerical invariants for 2-blocks with metacyclic defect groups. This paper is a part of the author's PhD thesis.

math.GR↗