Schur ring and quasi-simple modules

• Domínguez Wade, Pedro ^[1]
  1. [1] Universidad de Matanzas

     Universidad de Matanzas

     Cuba

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 28, Nº. 2, 2009, págs. 133-139
• Idioma: inglés
• DOI: 10.4067/S0716-09172009000200003
• Enlaces
  • Texto completo
• Resumen

  • Let R be a ring of algebraic integers of an algebraic number field F and let G ≤ GLn(R) be a finite group. In this paper we show that the R-span of G is just the matrix ring Mn(R) of the n X n-matrices over R if and only if G/Opi(G) is absolutely simple for all pi ∈ π, where π is the set of the positive prime divisors of |G| and Opi(G) is the largest normal pi-subgroup.

• Referencias bibliográficas
  • Citas [1] P. Huu Tiep. Globally irreducible representations of the finite symplectic group Sp4(q), Comm. in Algebra 22, pp. 6439 - 6457,...
  • [2] P. Huu Tiep. Basic spin representations of 2Sn and 2An as globally irreducible representations, Archiv Math. 64, pp. 103 - 112, (1995).
  • [3] P. Huu Tiep. Weil representations as globally irreducible representations, Math. Nachr. 184, pp. 313 - 327, (1997).
  • [4] P. Huu Tiep. Globally irreducible representations of finite groups and integral lattices, Geomet. Dedicata 64, pp. 85 - 123, (1997).
  • [5] P. Spiga and Q. Wang An answer to Hirasaka and Muzychuk : Every p-Schurring over C3 p p is Schurian, Discrete Mathematics 308, pp. 1760-1763,...
  • [6] A. E. Zalesskii and F.Van Oystaeyen Finite Groups over Arithmetical Rings and Globally Irreducible Representations, J. Algebra 215, pp....