Details
| Original language | English |
|---|---|
| Pages (from-to) | 855-870 |
| Number of pages | 16 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 69 |
| Issue number | 3 |
| Publication status | Published - 1 Sept 2018 |
| Externally published | Yes |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Quarterly Journal of Mathematics, Vol. 69, No. 3, 01.09.2018, p. 855-870.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Loewy lengths of centers of blocks
AU - Külshammer, Burkhard
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).
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054153675&partnerID=8YFLogxK
U2 - 10.1093/qmath/hay001
DO - 10.1093/qmath/hay001
M3 - Article
AN - SCOPUS:85054153675
VL - 69
SP - 855
EP - 870
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 3
ER -