Schur ring and quasi-simple modules
DOI:
https://doi.org/10.4067/S0716-09172009000200003Keywords:
Schur ring, π-globally simple.Abstract
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.References
[1] P. Huu Tiep. Globally irreducible representations of the finite symplectic group Sp4(q), Comm. in Algebra 22, pp. 6439 - 6457, (1994).
[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, (2008).
[6] A. E. Zalesskii and F.Van Oystaeyen Finite Groups over Arithmetical Rings and Globally Irreducible Representations, J. Algebra 215, pp. 418-436, (1999).
[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, (2008).
[6] A. E. Zalesskii and F.Van Oystaeyen Finite Groups over Arithmetical Rings and Globally Irreducible Representations, J. Algebra 215, pp. 418-436, (1999).
How to Cite
[1]
P. Domínguez Wade, “Schur ring and quasi-simple modules”, Proyecciones (Antofagasta, On line), vol. 28, no. 2, pp. 133-139, 1.
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