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Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ] Z/p , is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W). A set of(More)
Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V ] G , has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ] G. We use these methods to analyse k[2V 3 ] U 3 where U(More)
This 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 of m copies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré(More)
Ž. We study the depth of the ring of invariants of SL F acting on the nth 2 p symmetric power of the natural two-dimensional representation for n-p. These Ž. symmetric power representations are the irreducible representations of SL F 2 p over F. We prove that, when the greatest common divisor of p y 1 and n is less p than or equal to 2, the depth of the(More)
In this paper, we study the vector invariants, F[m V 2 ] Cp , of the 2-dimensional indecomposable representation V 2 of the cylic group, C p , of order p over a field F of characteristic p. This ring of invariants was first studied by David Richman [18] who showed that this ring required a generator of degree m(p − 1), thus demonstrating that the result of(More)