Invariant Theory of Finite Groups

1992 ◽  
pp. 306-344
Author(s):  
David Cox ◽  
John Little ◽  
Donal O’Shea
Keyword(s):  
Finite Groups ◽  
Invariant Theory

Invariant Theory of Finite Groups

1997 ◽  
pp. 311-348
Author(s):  
David Cox ◽  
John Little ◽  
Donal O’Shea
Keyword(s):  
Finite Groups ◽  
Invariant Theory

scholarly journals Non Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants

1999 ◽  
Vol 42 (2) ◽  
pp. 155-161 ◽  
Author(s):  
H. E. A. Campbell ◽  
A. V. Geramita ◽  
I. P. Hughes ◽  
R. J. Shank ◽  
D. L. Wehlau
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
Invariant Theory ◽  
Upper Bounds ◽  
Poincaré Series ◽  
Faithful Representation ◽  
Gorenstein Ring ◽  
Poincare Series ◽  
Trivial Group

AbstractThis paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants ofmcopies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré series methods to produce upper bounds for the degrees of the generators for the ring of invariants as long as that ring is Gorenstein. We prove that, for a finite non-trivial group G and a faithful representation of dimension n with n > 1, if the ring of invariants is Gorenstein then the ring is generated in degrees less than or equal to n(|G| − 1). If the ring of invariants is a hypersurface, the upper bound can be improved to |G|.

Modular Vector Invariants of Cyclic Permutation Representations

1999 ◽  
Vol 42 (1) ◽  
pp. 125-128 ◽  
Author(s):  
Larry Smith
Keyword(s):  
Prime Ideal ◽  
Cyclic Group ◽  
Finite Groups ◽  
Invariant Theory ◽  
Prime Order ◽  
Polynomial Algebra ◽  
Cyclic Permutation ◽  
Quotient Algebra ◽  
Chern Classes ◽  
Transfer Homomorphism

AbstractVector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group of prime order in characteristic p the image of the transfer homomorphism is a prime ideal, and the quotient algebra is a polynomial algebra on the top Chern classes of the action.

scholarly journals The Noether Bound in Invariant Theory of Finite Groups

2000 ◽  
Vol 156 (1) ◽  
pp. 23-32 ◽  
Author(s):  
Peter Fleischmann
Keyword(s):  
Finite Groups ◽  
Invariant Theory

E. Noether's bound in the invariant theory of finite groups

1996 ◽  
Vol 66 (2) ◽  
pp. 89-92 ◽  
Author(s):  
Larry Smith
Keyword(s):  
Finite Groups ◽  
Invariant Theory
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