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ON GENERATORS OF MODULAR INVARIANT RINGS OF FINITE GROUPS

Published online by Cambridge University Press:  01 September 1997

P. FLEISCHMANN  and
W. LEMPKEN
P. FLEISCHMANN
Affiliation:
Institute for Experimental Mathematics, University of Essen, Ellernstrasse 29, 45326 Essen, Germany
W. LEMPKEN
Affiliation:
Institute for Experimental Mathematics, University of Essen, Ellernstrasse 29, 45326 Essen, Germany
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Abstract

Let G be a finite group, let V be an [ ]G-module of finite dimension d, and denote by β(V, G) the minimal number m such that the invariant ring S(V)G is generated by finitely many elements of degree at most m. A classical result of E. Noether says that β(V, G)[les ][mid ]G[mid ] provided that char [ ] is coprime to [mid ]G[mid ]!. If char [ ] divides [mid ]G[mid ], then no bounds for β(V, G) are known except for very special choices of G. In this paper we present a constructive proof of the following. If H[les ]G with [G[ratio ]H]∈[ ]*, and if the restriction V[mid ]H is a permutation module (for example, if V is a projective [ ]G-module and H∈Sylp(G)), then β(V, G)[les ]max{[mid ]G[mid ], d([mid ]G[mid ]−1)} regardless of char [ ].

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 585 - 591
Copyright
© The London Mathematical Society 1997

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