Details
| Original language | English |
|---|---|
| Pages (from-to) | 1717-1732 |
| Number of pages | 16 |
| Journal | Algebras and representation theory |
| Volume | 16 |
| Issue number | 6 |
| Publication status | Published - Dec 2013 |
| Externally published | Yes |
Abstract
We determine the numerical invariants of blocks with defect group Q 2n × C2m and SD2n × C2m, where Q2n denotes a quaternion group of order 2n, C2m denotes a cyclic group of order 2m, and SD2n denotes a semidihedral group of order 2n. This generalizes Olsson's results for m = 0. As a consequence, we prove Brauer's k(B)- Conjecture, Olsson's Conjecture, Brauer's Height-Zero Conjecture, the Alperin- McKay Conjecture, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture for these blocks.Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119-125, 2012; Proc Amer Math Soc, 2012).
Keywords
- 2-blocks, Alperin'sWeight Conjecture, Ordinary weight conjecture, Quaternion defect groups, Semidihedral defect groups
ASJC Scopus subject areas
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In: Algebras and representation theory, Vol. 16, No. 6, 12.2013, p. 1717-1732.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Blocks with defect group Q2n × C2m and SD 2n × C2m
AU - Sambale, Benjamin
N1 - Funding Information: This work was partly supported by the “Deutsche Forschungsgemeinschaft”.
PY - 2013/12
Y1 - 2013/12
N2 - We determine the numerical invariants of blocks with defect group Q 2n × C2m and SD2n × C2m, where Q2n denotes a quaternion group of order 2n, C2m denotes a cyclic group of order 2m, and SD2n denotes a semidihedral group of order 2n. This generalizes Olsson's results for m = 0. As a consequence, we prove Brauer's k(B)- Conjecture, Olsson's Conjecture, Brauer's Height-Zero Conjecture, the Alperin- McKay Conjecture, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture for these blocks.Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119-125, 2012; Proc Amer Math Soc, 2012).
AB - We determine the numerical invariants of blocks with defect group Q 2n × C2m and SD2n × C2m, where Q2n denotes a quaternion group of order 2n, C2m denotes a cyclic group of order 2m, and SD2n denotes a semidihedral group of order 2n. This generalizes Olsson's results for m = 0. As a consequence, we prove Brauer's k(B)- Conjecture, Olsson's Conjecture, Brauer's Height-Zero Conjecture, the Alperin- McKay Conjecture, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture for these blocks.Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119-125, 2012; Proc Amer Math Soc, 2012).
KW - 2-blocks
KW - Alperin'sWeight Conjecture
KW - Ordinary weight conjecture
KW - Quaternion defect groups
KW - Semidihedral defect groups
UR - http://www.scopus.com/inward/record.url?scp=84892685433&partnerID=8YFLogxK
U2 - 10.1007/s10468-012-9379-6
DO - 10.1007/s10468-012-9379-6
M3 - Article
AN - SCOPUS:84892685433
VL - 16
SP - 1717
EP - 1732
JO - Algebras and representation theory
JF - Algebras and representation theory
SN - 1386-923X
IS - 6
ER -