In this thesis we study the invariant rings for the Sylow p-subgroups of the finite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3, IF,,) and GU(4, IF,, ), the symplectic group Sp(4,IF,) and the orthogonal group Q+(4,IF,) with q odd. In all cases, we obtained a minimal gene~ating set which is also a SAGEl 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, t he same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant fields for the Sylow p-subgroups of GU(n,IF,,), Sp(2n,IF,), Q+(2n,IF,), Q-(2n + 2, IF,) and Q(2n + 1, IF,), 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:594198 |
| Date | January 2011 |
| Creators | Ferreira, Jorge Nelio Marques |
| Publisher | University of Kent |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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