Browsing by Subject "Vector invariants"
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Item Open Access Modular vector invariants(2006) Madran, UğurVector 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.Item Open Access Vector invariants of permutation groups in characteristic zero(World Scientific Publishing Co. Pte. Ltd., 2023-12-21) Reimers, F.; Sezer, MüfitWe consider a finite permutation group acting naturally on a vector space V over a field k. A well-known theorem of G¨obel asserts that the corresponding ring of invariants k[V ] G is generated by the invariants of degree at most `dim V 2 ´ . In this paper, we show that if the characteristic of k is zero, then the top degree of vector coinvariants k[V m]G is also bounded above by `dim V 2 ´ , which implies the degree bound `dim V 2 ´ + 1 for the ring of vector invariants k[V m] G. So, G¨obel’s bound almost holds for vector invariants in characteristic zero as well.