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Explicit Generators of the Invariants of Finite Groups

✍ Scribed by David R. Richman

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
681 KB
Volume
124
Category
Article
ISSN
0001-8708

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✦ Synopsis

Let R denote a commutative (and associative) ring with 1 and let A denote a finitely generated commutative R-algebra. Let G denote a finite group of R-algebra automorphisms of A. In the case that R is a field of characteristic 0, Noether constructed a finite set of R-algebra generators of the invariants of G. This paper proves that the same construction produces a set of generators of the invariants of G when |G|! is invertible in R. Generators of the invariants of G are also explicitly described in the case that G is solvable and |G| is invertible in R.

1996 Academic Press, Inc.

Noether's proof is an ingenious application of the theorem (due to Waring [18, p. 13]) that the symmetric polynomials are generated by the elementary symmetric polynomials. A different proof of (0.1) is described in [19, pp. 275 276], but it is not as short or as direct as Noether's original proof.

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