Utilize este identificador para referenciar este registo:
http://hdl.handle.net/10400.13/177
Título: | On invariant Rings of Sylow subgroups of finite classical groups |
Autor: | Ferreira, Jorge Nélio Marques |
Orientador: | Peter Fleischmann |
Palavras-chave: | Modular invariant theory Finite classical groups p-Groups Invariant fields Invariant rings SAGBI Bases Complete Intersections . |
Data de Defesa: | 2011 |
Editora: | University of Kent |
Resumo: | In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups. |
Peer review: | yes |
URI: | http://hdl.handle.net/10400.13/177 |
Aparece nas colecções: | Teses de Doutoramento |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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DoutoramentoJorgeFerreira.pdf | 592,5 kB | Adobe PDF | Ver/Abrir |
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