In:
Nagoya Mathematical Journal, Cambridge University Press (CUP), Vol. 234 ( 2019-06), p. 127-138
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 $LL(ZB)\geqslant \min \{p^{d-1},4p^{d-2}\}$ . This extends some results previously obtained by the present authors. Moreover, we characterize blocks with uniserial center.
Type of Medium:
Online Resource
ISSN:
0027-7630
,
2152-6842
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2019
detail.hit.zdb_id:
2186888-8
SSG:
17,1
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