Loewy lengths of centers of blocks
Representation Theory
2016-09-14 v2
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)\le 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)\ge |D|/2.
Cite
@article{arxiv.1607.06241,
title = {Loewy lengths of centers of blocks},
author = {Burkhard Külshammer and Benjamin Sambale},
journal= {arXiv preprint arXiv:1607.06241},
year = {2016}
}
Comments
12 pages, several new results added