Details
| Original language | English |
|---|---|
| Pages (from-to) | 261-284 |
| Number of pages | 24 |
| Journal | Journal of algebra |
| Volume | 337 |
| Issue number | 1 |
| Publication status | Published - 1 Jul 2011 |
| Externally published | Yes |
Abstract
We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by Rédei (see Rédei, 1947 [41]). If the defect group is also metacyclic, then the block invariants are known (see Sambale [43]). In the remaining cases there are only two (infinite) families of 'interesting' defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and Olsson's conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture are satisfied. This paper is a part of the author's PhD thesis.
Keywords
- Alperin's conjecture, Blocks of finite groups, Dade's conjecture, Minimal nonabelian defect groups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 337, No. 1, 01.07.2011, p. 261-284.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - 2-Blocks with minimal nonabelian defect groups
AU - Sambale, Benjamin
PY - 2011/7/1
Y1 - 2011/7/1
N2 - We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by Rédei (see Rédei, 1947 [41]). If the defect group is also metacyclic, then the block invariants are known (see Sambale [43]). In the remaining cases there are only two (infinite) families of 'interesting' defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and Olsson's conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture are satisfied. This paper is a part of the author's PhD thesis.
AB - We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by Rédei (see Rédei, 1947 [41]). If the defect group is also metacyclic, then the block invariants are known (see Sambale [43]). In the remaining cases there are only two (infinite) families of 'interesting' defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and Olsson's conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture are satisfied. This paper is a part of the author's PhD thesis.
KW - Alperin's conjecture
KW - Blocks of finite groups
KW - Dade's conjecture
KW - Minimal nonabelian defect groups
UR - http://www.scopus.com/inward/record.url?scp=79956272572&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2011.02.006
DO - 10.1016/j.jalgebra.2011.02.006
M3 - Article
AN - SCOPUS:79956272572
VL - 337
SP - 261
EP - 284
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
IS - 1
ER -