Year: 2010
Type: article
Abstract: Let k k be an algebraically closed field of characteristic 2 2 , and let G G be a finite group. Suppose B B is a block of k G kG with dihedral defect groups such that there are precisely two isomorphism classes of simple B B -modules. The description by Erdmann of the quiver and relations of the basic algebra of B B is usually only given up to a certain parameter c c whose value is either 0 0 or 1 1 . In this article, we show that c = 0 c=0 if there exists a central extension G ^ \hat {G} of G G by a group of order 2 2 together with a block B ^ \hat {B} of k G ^ k\hat {G} with generalized quaternion defect groups such that B B
Author: Frauke Bleher
Institution: University of Iowa
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2022456778