Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-138 |
| Number of pages | 12 |
| Journal | Nagoya mathematical journal |
| Volume | 234 |
| Publication status | Published - 1 Jun 2019 |
| Externally published | Yes |
Abstract
Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by |D|/p+p-1 provided D is not cyclic. If D is nonabelian, we prove the stronger bound LL(ZB) < min{p d-1 , 4p d-2 } where |D|=p d . Conversely, we classify the blocks B with LL(ZB) ≥ min{p d-1 , 4p d-2 }. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Nagoya mathematical journal, Vol. 234, 01.06.2019, p. 127-138.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - LOEWY LENGTHS OF CENTERS OF BLOCKS II
AU - Külshammer, Burkhard
AU - Otokita, Yoshihiro
AU - Sambale, Benjamin
N1 - Funding information: The third author is supported by the German Research Foundation (project SA 2864/ 1-1) and the Daimler and Benz Foundation (project 32-08/13).
PY - 2019/6/1
Y1 - 2019/6/1
N2 - Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by |D|/p+p-1 provided D is not cyclic. If D is nonabelian, we prove the stronger bound LL(ZB) < min{p d-1 , 4p d-2 } where |D|=p d . Conversely, we classify the blocks B with LL(ZB) ≥ min{p d-1 , 4p d-2 }. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.
AB - Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by |D|/p+p-1 provided D is not cyclic. If D is nonabelian, we prove the stronger bound LL(ZB) < min{p d-1 , 4p d-2 } where |D|=p d . Conversely, we classify the blocks B with LL(ZB) ≥ min{p d-1 , 4p d-2 }. This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.
UR - http://www.scopus.com/inward/record.url?scp=85064853864&partnerID=8YFLogxK
U2 - 10.1017/nmj.2017.36
DO - 10.1017/nmj.2017.36
M3 - Article
AN - SCOPUS:85064853864
VL - 234
SP - 127
EP - 138
JO - Nagoya mathematical journal
JF - Nagoya mathematical journal
SN - 0027-7630
ER -