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The Noether Bound in Invariant Theory of Finite Groups

✍ Scribed by Peter Fleischmann

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 133 KB
Volume: 156
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1952

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✦ Synopsis

Let R be a commutative ring, V a finitely generated free R-module and G GL R (V) a finite group acting naturally on the graded symmetric algebra A=Sym(V). Let ;(A G ) denote the minimal number m, such that the ring A G of invariants can be generated by finitely many elements of degree at most m. Furthermore, let H dG be a normal subgroup such that the index |G : H | is invertible in R. In this paper we prove the inequality

For H=1 and |G | invertible in R we obtain Noether's bound ;(A G ) |G|, which so far had been shown for arbitrary groups only under the assumption that the factorial of the group order, |G|!, is invertible in R.

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