Oh the maximality of sp(l) in spn(k)

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...

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Autores:: Allan, Nelo

Tipo de recurso:: Article of journal

Fecha de publicación:: 1970

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Allan, Nelo481c6c34-8c37-402a-98c9-16fd4407f5773002019-06-28T10:34:36Z2019-06-28T10:34:36Z1970https://repositorio.unal.edu.co/handle/unal/42156http://bdigital.unal.edu.co/32253/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.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/31735Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 4, núm. 1 (1970); 7-15 0034-7426Allan, Nelo (1970) Oh the maximality of sp(l) in spn(k). Revista Colombiana de Matemáticas; Vol. 4, núm. 1 (1970); 7-15 0034-7426 .5 Ciencias naturales y matemáticas / Science51 Matemáticas / MathematicsQuotient fielddedekind domainsymplectic groupfinite indexfinitelyOh the maximality of sp(l) in spn(k)Artículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL31735-115779-1-PB.pdfapplication/pdf2978883https://repositorio.unal.edu.co/bitstream/unal/42156/1/31735-115779-1-PB.pdfc95444586906a20fbd0e92e26ea9a65dMD51THUMBNAIL31735-115779-1-PB.pdf.jpg31735-115779-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg8901https://repositorio.unal.edu.co/bitstream/unal/42156/2/31735-115779-1-PB.pdf.jpg6f899ea917f2b9851ccd83e86993644aMD52unal/42156oai:repositorio.unal.edu.co:unal/421562023-02-06 23:13:27.254Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	Oh the maximality of sp(l) in spn(k)
title	Oh the maximality of sp(l) in spn(k)
spellingShingle	Oh the maximality of sp(l) in spn(k) 5 Ciencias naturales y matemáticas / Science 51 Matemáticas / Mathematics Quotient field dedekind domain symplectic group finite index finitely
title_short	Oh the maximality of sp(l) in spn(k)
title_full	Oh the maximality of sp(l) in spn(k)
title_fullStr	Oh the maximality of sp(l) in spn(k)
title_full_unstemmed	Oh the maximality of sp(l) in spn(k)
title_sort	Oh the maximality of sp(l) in spn(k)
dc.creator.fl_str_mv	Allan, Nelo
dc.contributor.author.spa.fl_str_mv	Allan, Nelo
dc.subject.ddc.spa.fl_str_mv	5 Ciencias naturales y matemáticas / Science 51 Matemáticas / Mathematics
topic	5 Ciencias naturales y matemáticas / Science 51 Matemáticas / Mathematics Quotient field dedekind domain symplectic group finite index finitely
dc.subject.proposal.spa.fl_str_mv	Quotient field dedekind domain symplectic group finite index finitely
description	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.
publishDate	1970
dc.date.issued.spa.fl_str_mv	1970
dc.date.accessioned.spa.fl_str_mv	2019-06-28T10:34:36Z
dc.date.available.spa.fl_str_mv	2019-06-28T10:34:36Z
dc.type.spa.fl_str_mv	Artículo de revista
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url	https://repositorio.unal.edu.co/handle/unal/42156 http://bdigital.unal.edu.co/32253/
dc.language.iso.spa.fl_str_mv	spa
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dc.relation.spa.fl_str_mv	http://revistas.unal.edu.co/index.php/recolma/article/view/31735
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv	Revista Colombiana de Matemáticas; Vol. 4, núm. 1 (1970); 7-15 0034-7426
dc.relation.references.spa.fl_str_mv	Allan, Nelo (1970) Oh the maximality of sp(l) in spn(k). Revista Colombiana de Matemáticas; Vol. 4, núm. 1 (1970); 7-15 0034-7426 .
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
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dc.rights.license.spa.fl_str_mv	Atribución-NoComercial 4.0 Internacional
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rights_invalid_str_mv	Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2
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Oh the maximality of sp(l) in spn(k)

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