On Picent for blocks with normal defect group

2020/02/24 by Michael Livesey, Livesey, Michael, Claudio Marchi +1
Mathematics · #20C20 (Primary) 16D90 (Secondary) #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D90 #msc:20C20

paper · pdf · doi:10.48550/arxiv.2002.10571

arxiv created 2020/02/24 · arxiv updated 2020/02/26

Abstract

We prove that if b is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then Picent(b) is trivial. We also provide examples of blocks b of finite groups with non-trivial Picent(b). We even have examples with normal abelian defect group and abelian inertial quotient.

Related

• Some examples of Picard groups of blocks
• On Picard groups of blocks with normal defect groups
• Picard groups for some blocks with TI defect groups
• Classifying blocks with abelian defect groups of rank 3 for the prime 2
• Structure of blocks with normal defect and abelian p' inertial quotient