Browsing by Subject "Polynomial invariants"

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    Modular vector invariants
    (2006) Madran, Uğur
    Vector invariants of finite groups (see the introduction for definitions) provides, in general, counterexamples for many properties of the invariant theory when the characteristic of the ground field divides the group order. Noether number is such property. In this thesis, we improve a lower bound for Noether number given by Richman in 1996: namely, we give a lower bound depending on the Jordan canonical form of an element of order equal to characteristic of the field. This method yields an effective bound by means of simple arithmetic arguments. The results are valid for any faithful representation of the group, including reducible and irreducible ones. Also they are extended to any algebraic field extensions provided the characteristic of the field divides the group order.
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    On a theorem of gobel on permutation invariants
    (2008) Sezer, M.
    Let F be a field, let S = F[X1,..., Xn] be a polynomial ring on variables X1,..., Xn, and let G be a group of permutations of {X1,..., Xn}. Gobel proved that for n ≥ 3 the ring of invariants SG is generated by homogeneous elements of degree at most [image omitted]. In this article, we obtain reductions in the set of generators introduced by Gobel and sharpen his bound for almost all permutation groups over any ground field. Copyright © Taylor & Francis Group, LLC.
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    Orbit sums and modular vector invariants
    (2008) Stepanov, S.A.
    [No abstract available]