TY - JOUR

T1 - On centers of blocks with one simple module

AU - Landrock, Pierre

AU - Sambale, Benjamin

N1 - Funding information: The second author is supported by the German Research Foundation (project SA 2864/1-1) and the Daimler and Benz Foundation (project 32-08/13). Parts of this work will contribute the first author's PhD thesis which he currently writes under the supervision of Burkhard Külshammer.

PY - 2017/2/15

Y1 - 2017/2/15

N2 - Let G be a finite group, and let B be a non-nilpotent block of G with respect to an algebraically closed field of characteristic 2. Suppose that B has an elementary abelian defect group of order 16 and only one simple module. The main result of this paper describes the algebra structure of the center of B. This is motivated by a similar analysis of a certain 3-block of defect 2 in Kessar (2012) [15].

AB - Let G be a finite group, and let B be a non-nilpotent block of G with respect to an algebraically closed field of characteristic 2. Suppose that B has an elementary abelian defect group of order 16 and only one simple module. The main result of this paper describes the algebra structure of the center of B. This is motivated by a similar analysis of a certain 3-block of defect 2 in Kessar (2012) [15].

KW - Abelian defect

KW - Center of block algebra

KW - One Brauer character

UR - http://www.scopus.com/inward/record.url?scp=85004009685&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2016.10.046

DO - 10.1016/j.jalgebra.2016.10.046

M3 - Article

AN - SCOPUS:85004009685

VL - 472

SP - 339

EP - 368

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

ER -