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Broué's Abelian defect group conjecture holds for the Janko simple group J4

  • Autores: Shigeo Koshitani, Naoko Kunugi, Katsushi Waki
  • Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 6, 2008, págs. 1438-1456
  • Idioma: inglés
  • DOI: 10.1016/j.jpaa.2007.10.006
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • In the representation theory of finite groups, there is a well known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an Abelian defect group P, then A and its Brauer corresponding block B of the normalizer NG(P) of P in G are equivalent (Rickard equivalent). This conjecture is called Broué�s Abelian defect group conjecture. We prove in this paper that Broué�s Abelian defect group conjecture is true for a non-principal 3-block A with an elementary Abelian defect group P of order 9 of the Janko simple group J4. It then turns out that Broué's Abelian defect group conjecture holds for all primes p and for all p-blocks of the Janko simple group J4.


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