Details
| Original language | English |
|---|---|
| Pages (from-to) | 2241-2273 |
| Number of pages | 33 |
| Journal | Algebra and Number Theory |
| Volume | 7 |
| Issue number | 9 |
| Publication status | Published - 2013 |
| Externally published | Yes |
Abstract
We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
Keywords
- 2-blocks, Alperin's weight conjecture, Bicyclic defect groups, Brauer's k.B/-conjecture
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Algebra and Number Theory, Vol. 7, No. 9, 2013, p. 2241-2273.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Further evidence for conjectures in block theory
AU - Sambale, Benjamin
PY - 2013
Y1 - 2013
N2 - We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
AB - We prove new inequalities concerning Brauer's k(B)-conjecture and Olsson's conjecture by generalizing old results. After that, we obtain the invariants for 2-blocks of finite groups with certain bicyclic defect groups. Here, a bicyclic group is a product of two cyclic subgroups. This provides an application for the classification of the corresponding fusion systems in a previous paper. To some extent, this generalizes previously known cases with defect groups of types D2n × C2m, Q2n × C2m and D2n * C2m. As a consequence, we prove Alperin's weight conjecture and other conjectures for several new infinite families of nonnilpotent blocks. We also prove Brauer's k(B)-conjecture and Olsson's conjecture for the 2-blocks of defect at most 5. This completes results from a previous paper. The k(B)-conjecture is also verified for defect groups with a cyclic subgroup of index at most 4. Finally, we consider Olsson's conjecture for certain 3-blocks.
KW - 2-blocks
KW - Alperin's weight conjecture
KW - Bicyclic defect groups
KW - Brauer's k.B/-conjecture
UR - http://www.scopus.com/inward/record.url?scp=84892698451&partnerID=8YFLogxK
U2 - 10.2140/ant.2013.7.2241
DO - 10.2140/ant.2013.7.2241
M3 - Article
AN - SCOPUS:84892698451
VL - 7
SP - 2241
EP - 2273
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 9
ER -