Loewy lengths of centers of blocks

2016/07/21 by Külshammer, Burkhard, Sambale, Benjamin
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1607.06241

Abstract

Let B be a block of a finite group with respect to an algebraically closed field F of characteristic p>0. In a recent paper, Otokita gave an upper bound for the Loewy length LL(ZB) of the center ZB of B in terms of a defect group D of B. We refine his methods in order to prove the optimal bound LL(ZB)≤ LL(FD) whenever D is abelian. We also improve Otokita's bound for non-abelian defect groups. As an application we classify the blocks B such that LL(ZB)≥ |D|/2.

Related

• Loewy lengths of centers of blocks and exponents of defect groups
• On centers of blocks with non-cyclic defect groups
• Some studies on Loewy lengths of centers of p-blocks
• Loewy lengths of blocks with abelian defect groups
• Notes on Loewy series of centers of p-blocks