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Publication
On invariant Rings of Sylow subgroups of finite classical groups
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Advisor(s)
Abstract(s)
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.
Description
Keywords
Modular invariant theory Finite classical groups p-Groups Invariant fields Invariant rings SAGBI Bases Complete Intersections .