The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Ferreira, Jorge N. M.; Fleischmann, Peter

http://hdl.handle.net/10400.13/5033

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Authors

Ferreira, Jorge N. M.

Fleischmann, Peter

Abstract(s)

Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.

Keywords

Invariant rings SAGBI bases Modular invariant theory Sylow subgroups Finite classical groups . Faculdade de Ciências Exatas e da Engenharia

URI

http://hdl.handle.net/10400.13/5033

Citation

Ferreira, J. N., & Fleischmann, P. (2017). The invariant rings of the Sylow groups of GU (3, q2), GU (4, q2), Sp (4, q) and O+ (4, q) in the natural characteristic. Journal of Symbolic Computation, 79, 356-371.