Details
| Original language | English |
|---|---|
| Pages (from-to) | 481-507 |
| Number of pages | 27 |
| Journal | Pacific journal of mathematics |
| Volume | 262 |
| Issue number | 2 |
| Publication status | Published - 2013 |
| Externally published | Yes |
Abstract
We prove that Brauer's height zero conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and p-rational irreducible characters. The Alperin-McKay conjecture then follows provided p = 3. Along the way we verify a few other conjectures. Finally we consider more closely the extraspecial defect group of order p3 and exponent p2 for an odd prime. Here for blocks with inertial index 2 we prove the Galois-Alperin-McKay conjecture by computing k0.B/. Then for p ≤ 11 also Alperin's weight conjecture follows. This improves results of Gao (2012), Holloway, Koshitani, Kunugi (2010) and Hendren (2005).
Keywords
- Alperin's weight conjecture, Brauer's height zero conjecture, Metacyclic defect groups
ASJC Scopus subject areas
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In: Pacific journal of mathematics, Vol. 262, No. 2, 2013, p. 481-507.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Brauer's height zero conjecture for metacyclic defect groups
AU - Sambale, Benjamin
PY - 2013
Y1 - 2013
N2 - We prove that Brauer's height zero conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and p-rational irreducible characters. The Alperin-McKay conjecture then follows provided p = 3. Along the way we verify a few other conjectures. Finally we consider more closely the extraspecial defect group of order p3 and exponent p2 for an odd prime. Here for blocks with inertial index 2 we prove the Galois-Alperin-McKay conjecture by computing k0.B/. Then for p ≤ 11 also Alperin's weight conjecture follows. This improves results of Gao (2012), Holloway, Koshitani, Kunugi (2010) and Hendren (2005).
AB - We prove that Brauer's height zero conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and p-rational irreducible characters. The Alperin-McKay conjecture then follows provided p = 3. Along the way we verify a few other conjectures. Finally we consider more closely the extraspecial defect group of order p3 and exponent p2 for an odd prime. Here for blocks with inertial index 2 we prove the Galois-Alperin-McKay conjecture by computing k0.B/. Then for p ≤ 11 also Alperin's weight conjecture follows. This improves results of Gao (2012), Holloway, Koshitani, Kunugi (2010) and Hendren (2005).
KW - Alperin's weight conjecture
KW - Brauer's height zero conjecture
KW - Metacyclic defect groups
UR - http://www.scopus.com/inward/record.url?scp=84878705970&partnerID=8YFLogxK
U2 - 10.2140/pjm.2013.262.481
DO - 10.2140/pjm.2013.262.481
M3 - Article
AN - SCOPUS:84878705970
VL - 262
SP - 481
EP - 507
JO - Pacific journal of mathematics
JF - Pacific journal of mathematics
SN - 0030-8730
IS - 2
ER -