Details
| Original language | English |
|---|---|
| Pages (from-to) | 4057-4069 |
| Number of pages | 13 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 141 |
| Issue number | 12 |
| Publication status | Published - 2013 |
| Externally published | Yes |
Abstract
We determine the numerical invariants of blocks with defect group D2n *C2m ≅ Q2n *C2m (central product), where n ≥ 3 and m ≥ 2. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally Eaton'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 continues B. Sambale, Blocks with defect group D2n × C2m, J. Pure Appl. Algebra 216 (2012), 119-125.
Keywords
- 2-blocks, Alperin's weight conjecture, Dihedral defect groups, Ordinary weight conjecture
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Proceedings of the American Mathematical Society, Vol. 141, No. 12, 2013, p. 4057-4069.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Blocks with central product defect group D2n * C2m
AU - Sambale, Benjamin
PY - 2013
Y1 - 2013
N2 - We determine the numerical invariants of blocks with defect group D2n *C2m ≅ Q2n *C2m (central product), where n ≥ 3 and m ≥ 2. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally Eaton'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 continues B. Sambale, Blocks with defect group D2n × C2m, J. Pure Appl. Algebra 216 (2012), 119-125.
AB - We determine the numerical invariants of blocks with defect group D2n *C2m ≅ Q2n *C2m (central product), where n ≥ 3 and m ≥ 2. As a consequence, we prove Brauer's k(B)-conjecture, Olsson's conjecture (and more generally Eaton'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 continues B. Sambale, Blocks with defect group D2n × C2m, J. Pure Appl. Algebra 216 (2012), 119-125.
KW - 2-blocks
KW - Alperin's weight conjecture
KW - Dihedral defect groups
KW - Ordinary weight conjecture
UR - http://www.scopus.com/inward/record.url?scp=84884802969&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2013-11938-6
DO - 10.1090/S0002-9939-2013-11938-6
M3 - Article
AN - SCOPUS:84884802969
VL - 141
SP - 4057
EP - 4069
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -