Details
| Original language | English |
|---|---|
| Pages (from-to) | 513-526 |
| Number of pages | 14 |
| Journal | Israel journal of mathematics |
| Volume | 228 |
| Issue number | 2 |
| Publication status | Published - 1 Oct 2018 |
| Externally published | Yes |
Abstract
An open conjecture by Harada from 1981 gives an easy characterization of the p-blocks of a finite group in terms of the ordinary character table. Kiyota and Okuyama have shown that the conjecture holds for p-solvable groups. In the present work we extend this result using a criterion on the decomposition matrix. In this way we prove Harada’s Conjecture for several new families of defect groups and for all blocks of sporadic simple groups. In the second part of the paper we present a dual approach to Harada’s Conjecture.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Israel journal of mathematics, Vol. 228, No. 2, 01.10.2018, p. 513-526.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Remarks on Harada’s conjecture
AU - Sambale, Benjamin
N1 - Funding information: Acknowledgment. This work is supported by the German Research Foundation (project SA 2864/1-1) and the Daimler and Benz Foundation (project 32-08/13). The author thanks Eugenio Giannelli, Gunter Malle and Gabriel Navarro for interesting discussions on the subject.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - An open conjecture by Harada from 1981 gives an easy characterization of the p-blocks of a finite group in terms of the ordinary character table. Kiyota and Okuyama have shown that the conjecture holds for p-solvable groups. In the present work we extend this result using a criterion on the decomposition matrix. In this way we prove Harada’s Conjecture for several new families of defect groups and for all blocks of sporadic simple groups. In the second part of the paper we present a dual approach to Harada’s Conjecture.
AB - An open conjecture by Harada from 1981 gives an easy characterization of the p-blocks of a finite group in terms of the ordinary character table. Kiyota and Okuyama have shown that the conjecture holds for p-solvable groups. In the present work we extend this result using a criterion on the decomposition matrix. In this way we prove Harada’s Conjecture for several new families of defect groups and for all blocks of sporadic simple groups. In the second part of the paper we present a dual approach to Harada’s Conjecture.
UR - http://www.scopus.com/inward/record.url?scp=85053523804&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1772-3
DO - 10.1007/s11856-018-1772-3
M3 - Article
AN - SCOPUS:85053523804
VL - 228
SP - 513
EP - 526
JO - Israel journal of mathematics
JF - Israel journal of mathematics
SN - 0021-2172
IS - 2
ER -