Publication
On invariant Rings of Sylow subgroups of finite classical groups
| dc.contributor.advisor | Peter Fleischmann | |
| dc.contributor.author | Ferreira, Jorge Nélio Marques | |
| dc.date.accessioned | 2011-10-12T13:39:14Z | |
| dc.date.available | 2011-10-12T13:39:14Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | 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. | por |
| dc.identifier.uri | http://hdl.handle.net/10400.13/177 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | University of Kent | por |
| dc.subject | Modular invariant theory | por |
| dc.subject | Finite classical groups | por |
| dc.subject | p-Groups | por |
| dc.subject | Invariant fields | por |
| dc.subject | Invariant rings | por |
| dc.subject | SAGBI Bases | por |
| dc.subject | Complete Intersections | por |
| dc.subject | . | por |
| dc.title | On invariant Rings of Sylow subgroups of finite classical groups | por |
| dc.type | doctoral thesis | |
| dspace.entity.type | Publication | |
| person.familyName | Marques Ferreira | |
| person.givenName | Jorge Nélio | |
| person.identifier.orcid | 0000-0003-1364-5791 | |
| rcaap.rights | openAccess | por |
| rcaap.type | doctoralThesis | por |
| relation.isAuthorOfPublication | b136ee8d-f897-4ac6-a748-1fe2606bbbbf | |
| relation.isAuthorOfPublication.latestForDiscovery | b136ee8d-f897-4ac6-a748-1fe2606bbbbf |