Details
| Original language | English |
|---|---|
| Pages (from-to) | 411-422 |
| Number of pages | 12 |
| Journal | Results in mathematics |
| Volume | 71 |
| Issue number | 1-2 |
| Publication status | Published - 21 May 2016 |
| Externally published | Yes |
Abstract
Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p4. Then, we show that B satisfies Brauer’s k(B)-Conjecture (i.e. k(B) ≤ | D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.
Keywords
- Abelian defect groups, Blocks, Brauer’s k(B)-Conjecture, Defect 3
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
- Mathematics(all)
- Applied Mathematics
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In: Results in mathematics, Vol. 71, No. 1-2, 21.05.2016, p. 411-422.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Blocks with Abelian Defect Groups of Small Rank
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2016, Springer International Publishing.
PY - 2016/5/21
Y1 - 2016/5/21
N2 - Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p4. Then, we show that B satisfies Brauer’s k(B)-Conjecture (i.e. k(B) ≤ | D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.
AB - Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p4. Then, we show that B satisfies Brauer’s k(B)-Conjecture (i.e. k(B) ≤ | D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.
KW - Abelian defect groups
KW - Blocks
KW - Brauer’s k(B)-Conjecture
KW - Defect 3
UR - http://www.scopus.com/inward/record.url?scp=84969752801&partnerID=8YFLogxK
U2 - 10.1007/s00025-016-0557-4
DO - 10.1007/s00025-016-0557-4
M3 - Article
AN - SCOPUS:84969752801
VL - 71
SP - 411
EP - 422
JO - Results in mathematics
JF - Results in mathematics
SN - 1422-6383
IS - 1-2
ER -