{"id":42821,"date":"2018-03-09T09:44:54","date_gmt":"2018-03-09T09:44:54","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/extensiones-de-kg-modulos-irreducibles\/"},"modified":"2018-03-09T09:44:54","modified_gmt":"2018-03-09T09:44:54","slug":"extensiones-de-kg-modulos-irreducibles","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/extensiones-de-kg-modulos-irreducibles\/","title":{"rendered":"Extensiones de kg-modulos irreducibles."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Concepcion Martinez Perez <\/strong><\/h2>\n<p>En la memoria estudiamos extensiones de kg-m\u00f3dulos irreducibles. Si u y v son kg-m\u00f3dulos irreducibles, el n\u00famero de clases de equiValencia de extensiones de u por v es igual a la multiplicidad de v como factor de composici\u00f3n del segundo t\u00e9rmino de la serie descendente de loewy de la cubierta proyectiva de u. Esto se puede expresar desde un punto de vista cohomol\u00f3gico, lo que nos ha permitido utilizar t\u00e9cnicas de cohomolog\u00eda de grupos. Hemos dividido la memoria en dos partes, la primera dedicada a extensiones del m\u00f3dulo trivial de dimensi\u00f3n uno (k) y la segunda al caso general.  gracias al teorema de gaschutz, si g es p-resoluble, mediante la estructura principal de g se pueden determinar los m\u00f3dulos irreducibles v para los que existe una extensi\u00f3n no escindida de k por v, el n\u00famero de clases de equiValencia de estas extensiones y sus centralizadores. En la memoria probamos que, si g es un grupo cualquiera, estas cuestiones se pueden reducir al caso casi-simple, utilizando para ello un teorema de kov\u00e1cs. Tambi\u00e9n consideramos cuestiones relativas a determinados subgrupos caracter\u00edsticos de g definidos como la intersecci\u00f3n de los centralizadores de aquellos m\u00f3dulos irreducibles v que admiten una extensi\u00f3n de k por v de cierto tipo. Mediante estos subgrupos, caracterizamos diversas propiedades del grupo como la p-constricci\u00f3n.  respecto a la segunda parte, en la memoria comprobamos que tambi\u00e9n juega un papel fundamental la estructura principal de g. Damos una serie de condiciones en las que se puede determinar c\u00f3mo afecta un factor principal del grupo a las extensiones de un kg-m\u00f3dulo irreducible u. Algunas de estas condiciones proceden de la obtenci\u00f3n de un resultado de cohomolog\u00eda de inter\u00e9s en s\u00ed mismo. En particular, \u00e9stas condiciones se verifican si el m\u00f3dulo es proyectivo respecto al cociente del grupo con su centralizador. Por otra parte, proporcionamos una serie de contraejemplos para<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Extensiones de kg-modulos irreducibles.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Extensiones de kg-modulos irreducibles. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Concepcion Martinez Perez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 25\/03\/1999<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li> Jimenez Seral M. Paz<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Miguel Torres iglesias <\/li>\n<li>urs Stammbach (vocal)<\/li>\n<li>Francisco Perez monasor (vocal)<\/li>\n<li>wolfgang Willems (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Concepcion Martinez Perez En la memoria estudiamos extensiones de kg-m\u00f3dulos irreducibles. Si u y v son kg-m\u00f3dulos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2809,2807,126,11714,13610],"tags":[107342,11717,11920,11919,107343,11718],"class_list":["post-42821","post","type-post","status-publish","format-standard","hentry","category-algebra","category-grupos-generalidades","category-matematicas","category-teoria-de-la-representacion","category-zaragoza","tag-concepcion-Martinez-perez","tag-francisco-perez-monasor","tag-jimenez-seral-m-paz","tag-miguel-torres-iglesias","tag-urs-stammbach","tag-wolfgang-willems"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/42821","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=42821"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/42821\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=42821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=42821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=42821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}