Separating invariants for modular P-groups and groups acting diagonally

We study separating algebras for rings of invariants of finite groups. We describe a separating subalgebra for invariants of p-groups in characteristic p using only transfers and norms. Also we give an explicit construction of a finite separating set for invariants of groups acting diagonally. © International Press 2009

The noether map i

Let æ : G GL(n, F) be a faithful representation of a finite group G. In this paper we study the image of the associated Noether map J G G : F[V(G)]G → F [V]G. It turns out that the image of the Noether map characterizes the ring of invariants in the sense that its integral closure Im (JG G = F [V]G. This is true without any restrictions on the group, representation, or ground field. Moreover, we show that the extension Im(J G G) ⊆ F [V]G is a finite p-root extension if the characteristic of the ground field is p. Furthermore, we show that the Noether map is surjective, if V = Fn is a projective FG-module. We apply these results and obtain upper bounds on the degrees of a minimal generating set of FVG and the Cohen-Macaulay defect of FV G. We illustrate our results with several examples. © de Gruyter 2009

The invariants of modular indecomposable representations of ℤp 2

We consider the invariant ring for an indecomposable representation of a cyclic group of order p 2 over a field of characteristic p. We describe a set of -algebra generators of this ring of invariants, and thus derive an upper bound for the largest degree of an element in a minimal generating set for the ring of invariants. This bound, as a polynomial in p, is of degree two. © 2008 Springer-Verlag

Mme Bertin's Z/4 revisited

In this note it is shown that for p-regular representations the transfer is surjective in degrees prime to the characteristic of the ground field. In particular, for groups of order 2p in their regular representation and for Z/p in any permutation representation the image of the transfer together with (some of) the orbit chern classes generates the ring of invariants. This applies to one of Marie-Jose Bertin's famous examples. (orig.)Available from TIB Hannover: RR 4487(1997,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The Lasker-Noether theorem for P-invariant ideals

This article is motivated by the study of modular invariants of finite groups using as tools, the Steenrod algebra and the Dickson algebra. The ring of invariants F[V]"G of a representation #rho#:G#->#GL(n, F) of a finite group G over a Galois field F of characteristic p is an unstable graded connected commutative Noetherean algebra over the Steenrod algebra P"*. We adopt this more general point of view and study P"*-invariant ideals in unstable graded connected commutative Noetherean algebras H"* over a Galois field F. (An ideal I is contained in H"* is called P"*-invariant if it is closed under the action of the Steenrod algebra). Our goal is to show that P"*-invariant ideals have a P"*-invariant primary decomposition. (orig.)Available from TIB Hannover: RR 4487(1995,26) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Rings of generalized and stable invariants and classifying spaces of compact Lie groups

SIGLEAvailable from TIB Hannover: RR 4487(1996,14) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman