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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.28 n.2 Antofagasta ago. 2009

http://dx.doi.org/10.4067/S0716-09172009000200003 

Proyecciones Journal of Mathematics
Vol. 28, N° 2, pp. 133-139, August 2009.
Universidad Católica del Norte
Antofagasta - Chile



SCHUR RING AND QUASI-SIMPLE MODULES


Pedro Domínguez-Wade

Universidad De Matanzas, Cuba


Correspondencia a:


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 piπ, where π is the set of the positive prime divisors of |G| and Opi(G) is the largest normal pi-subgroup.

Subjclass : Primary 20C20 ; Secondary 19A22.

Keywords : Schur ring π-globally simple.



References

[1] P. Huu Tiep. Globally irreducible representations of the finite sym-plectic group Sp4(q), Comm. in Algebra 22, pp. 6439 - 6457, (1994).        [ Links ]

[2] P. Huu Tiep. Basic spin representations of 2Sn and 2An as globally irreducible representations, Archiv Math. 64, pp. 103 - 112, (1995).        [ Links ]

[3] P. Huu Tiep. Weil representations as globally irreducible representations, Math. Nachr. 184, pp. 313 - 327, (1997).        [ Links ]

[4] P. Huu Tiep. Globally irreducible representations of finite groups and integral lattices, Geomet. Dedicata 64, pp. 85 - 123, (1997).        [ Links ]

[5] P. Spiga and Q. Wang An answer to Hirasaka and Muzychuk : Every p-Schurri ng over C3p p is Schurian, Discrete Mathematics 308, pp. 1760-1763, (2008).        [ Links ]

[6] A. E. Zalesskii and F.Van Oystaeyen Finite Groups over Arithmetical Rings and Globally Irreducible Representations, J. Algebra 215, pp. 418-436, (1999).        [ Links ]

PEDRO DOMÍNGUEZ WADE
Department of Mathematics
Matanzas University
Carretera Matanzas
Varadero Km. 3
Cuba
e-mail : pedro.dominguez@umcc.cu


Received : November 2008. Accepted : April 2009