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Invariants of Finite Groups over Fields of Characteristicp

✍ Scribed by David R. Richman

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

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✦ Synopsis

Let V denote a finite-dimensional K vector space and let G denote a finite group of K-linear automorphisms of V. Let V m denote the direct sum of m copies of V and let G act on the symmetric algebra K[V m ] of V m by the diagonal action on V m . A result of Noether implies that, if char K=0, then K[V m ] G can be generated as a K-algebra by polynomials whose degrees are |G|, no matter how large m is. This paper proves that this result no longer holds when the characteristic of K divides |G|. More precisely, it is proved in this case that there is a positive number :, depending only on |G| and char K, such that every set of K-algebra generators of K[V m ] G contains a generator whose degree is :m.

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