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On Generators of Modular Invariant Rings of Finite Groups
Author(s) -
Fleischmann P.,
Lempken W.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939700341x
Subject(s) - mathematics , combinatorics , invariant (physics) , noether's theorem , local ring , finite group , knot (papermaking) , primitive permutation group , free module , discrete mathematics , pure mathematics , ring (chemistry) , group (periodic table) , symmetric group , lagrangian , cyclic permutation , chemistry , organic chemistry , chemical engineering , engineering , mathematical physics
Let G be a finite group, let V be an F 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 ) ⩽ ∣ G ∣ provided that char F is coprime to ∣ G ∣!. If char F divides ∣ G ∣, 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 ⩽ G with [ G : H ]∈F * , and if the restriction V ∣ H is a permutation module (for example, if V is a projective F G ‐module and H ∈Syl p ( G )), then β( V , G )⩽max{∣ G ∣, d (∣ G ∣−1)} regardless of char F. 1991 Mathematics Subject Classification 13A50, 20C20.