Details
| Original language | English |
|---|---|
| Pages (from-to) | 505-518 |
| Number of pages | 14 |
| Journal | Manuscripta mathematica |
| Volume | 146 |
| Issue number | 3-4 |
| Publication status | Published - Mar 2014 |
Abstract
For a block B of a finite group we prove that (Formula presented.) where k(B) [respectively l(B)] is the number of irreducible ordinary (respectively Brauer) characters of B, and C is the Cartan matrix of B. As an application, we show that Brauer’s k(B)-Conjecture holds for every block with abelian defect group D and inertial quotient T provided there exists an element u ∈ D such that CT(u) acts freely on (Formula presented.). This gives a new proof of Brauer’s Conjecture for abelian defect groups of rank at most 2. We also prove the conjecture in case (Formula presented.).
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In: Manuscripta mathematica, Vol. 146, No. 3-4, 03.2014, p. 505-518.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Cartan matrices and Brauer’s k(B)-conjecture III
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/3
Y1 - 2014/3
N2 - For a block B of a finite group we prove that (Formula presented.) where k(B) [respectively l(B)] is the number of irreducible ordinary (respectively Brauer) characters of B, and C is the Cartan matrix of B. As an application, we show that Brauer’s k(B)-Conjecture holds for every block with abelian defect group D and inertial quotient T provided there exists an element u ∈ D such that CT(u) acts freely on (Formula presented.). This gives a new proof of Brauer’s Conjecture for abelian defect groups of rank at most 2. We also prove the conjecture in case (Formula presented.).
AB - For a block B of a finite group we prove that (Formula presented.) where k(B) [respectively l(B)] is the number of irreducible ordinary (respectively Brauer) characters of B, and C is the Cartan matrix of B. As an application, we show that Brauer’s k(B)-Conjecture holds for every block with abelian defect group D and inertial quotient T provided there exists an element u ∈ D such that CT(u) acts freely on (Formula presented.). This gives a new proof of Brauer’s Conjecture for abelian defect groups of rank at most 2. We also prove the conjecture in case (Formula presented.).
KW - 20C15
KW - 20C20
UR - http://www.scopus.com/inward/record.url?scp=84922723624&partnerID=8YFLogxK
U2 - 10.1007/s00229-014-0702-x
DO - 10.1007/s00229-014-0702-x
M3 - Article
AN - SCOPUS:84922723624
VL - 146
SP - 505
EP - 518
JO - Manuscripta mathematica
JF - Manuscripta mathematica
SN - 0025-2611
IS - 3-4
ER -