Details
| Original language | English |
|---|---|
| Pages (from-to) | 555-570 |
| Number of pages | 16 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Volume | 156 |
| Issue number | 3 |
| Publication status | Published - May 2014 |
| Externally published | Yes |
Abstract
We give a lower bound on the Loewy length of a p-block of a finite group in terms of its defect. We then discuss blocks with small Loewy length. Since blocks with Loewy length at most 3 are known, we focus on blocks of Loewy length 4 and provide a relatively short list of possible defect groups. It turns out that p-solvable groups can only admit blocks of Loewy length 4 if p=2. However, we find (principal) blocks of simple groups with Loewy length 4 and defect 1 for all p ≡ 1 (mod 3). We also consider sporadic, symmetric and simple groups of Lie type in defining characteristic. Finally, we give stronger conditions on the Loewy length of a block with cyclic defect group in terms of its Brauer tree.
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In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 156, No. 3, 05.2014, p. 555-570.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Loewy lengths of blocks
AU - Koshitani, Shigeo
AU - Külshammer, Burkhard
AU - Sambale, Benjamin
PY - 2014/5
Y1 - 2014/5
N2 - We give a lower bound on the Loewy length of a p-block of a finite group in terms of its defect. We then discuss blocks with small Loewy length. Since blocks with Loewy length at most 3 are known, we focus on blocks of Loewy length 4 and provide a relatively short list of possible defect groups. It turns out that p-solvable groups can only admit blocks of Loewy length 4 if p=2. However, we find (principal) blocks of simple groups with Loewy length 4 and defect 1 for all p ≡ 1 (mod 3). We also consider sporadic, symmetric and simple groups of Lie type in defining characteristic. Finally, we give stronger conditions on the Loewy length of a block with cyclic defect group in terms of its Brauer tree.
AB - We give a lower bound on the Loewy length of a p-block of a finite group in terms of its defect. We then discuss blocks with small Loewy length. Since blocks with Loewy length at most 3 are known, we focus on blocks of Loewy length 4 and provide a relatively short list of possible defect groups. It turns out that p-solvable groups can only admit blocks of Loewy length 4 if p=2. However, we find (principal) blocks of simple groups with Loewy length 4 and defect 1 for all p ≡ 1 (mod 3). We also consider sporadic, symmetric and simple groups of Lie type in defining characteristic. Finally, we give stronger conditions on the Loewy length of a block with cyclic defect group in terms of its Brauer tree.
UR - http://www.scopus.com/inward/record.url?scp=84897113185&partnerID=8YFLogxK
U2 - 10.1017/S0305004114000103
DO - 10.1017/S0305004114000103
M3 - Article
AN - SCOPUS:84897113185
VL - 156
SP - 555
EP - 570
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 0305-0041
IS - 3
ER -