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 -