Publicado

1970-01-01

Oh the maximality of Sp(L) in Spn(k)

Palabras clave:


Quotient field, dedekind domain, symplectic group, finite index, finitely (es)

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Autores/as

  • Nelo Allan Universidad Nacional de Colombia

Let k be the quotient field of a Dedekind domain O, (k ≠ 0) and let G = Spn(k) be the Symplectic Group over k. G acts on the 2n -dimensional vector space V.

Let L be a lattice in V, and let Sp(L) be the stabilizer of L in Spn(k). Our

purpose is to investigate whether or not there exists a subgroup of Spn(k) which contains Sp(L) as a subgroup of finite index. Although in several points we need only weaker assumptions, to describe our methods we shall assume that all residue class fields of k are finite. First of all we would like to point out th at the 0-  module A(Sp(L),O) generated by Sp(L) in Mn(k). is an order, i.e., it is a subring which is a finitely generated 0-module and generates Mn(k) over k.

Cómo citar

APA

Allan, N. (1970). Oh the maximality of Sp(L) in Spn(k). Revista Colombiana de Matemáticas, 4(1), 7–15. https://revistas.unal.edu.co/index.php/recolma/article/view/31735

ACM

[1]
Allan, N. 1970. Oh the maximality of Sp(L) in Spn(k). Revista Colombiana de Matemáticas. 4, 1 (ene. 1970), 7–15.

ACS

(1)
Allan, N. Oh the maximality of Sp(L) in Spn(k). rev.colomb.mat 1970, 4, 7-15.

ABNT

ALLAN, N. Oh the maximality of Sp(L) in Spn(k). Revista Colombiana de Matemáticas, [S. l.], v. 4, n. 1, p. 7–15, 1970. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/31735. Acesso em: 29 mar. 2024.

Chicago

Allan, Nelo. 1970. «Oh the maximality of Sp(L) in Spn(k)». Revista Colombiana De Matemáticas 4 (1):7-15. https://revistas.unal.edu.co/index.php/recolma/article/view/31735.

Harvard

Allan, N. (1970) «Oh the maximality of Sp(L) in Spn(k)», Revista Colombiana de Matemáticas, 4(1), pp. 7–15. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/31735 (Accedido: 29 marzo 2024).

IEEE

[1]
N. Allan, «Oh the maximality of Sp(L) in Spn(k)», rev.colomb.mat, vol. 4, n.º 1, pp. 7–15, ene. 1970.

MLA

Allan, N. «Oh the maximality of Sp(L) in Spn(k)». Revista Colombiana de Matemáticas, vol. 4, n.º 1, enero de 1970, pp. 7-15, https://revistas.unal.edu.co/index.php/recolma/article/view/31735.

Turabian

Allan, Nelo. «Oh the maximality of Sp(L) in Spn(k)». Revista Colombiana de Matemáticas 4, no. 1 (enero 1, 1970): 7–15. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/31735.

Vancouver

1.
Allan N. Oh the maximality of Sp(L) in Spn(k). rev.colomb.mat [Internet]. 1 de enero de 1970 [citado 29 de marzo de 2024];4(1):7-15. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/31735

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