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Rings of invariants of modular p-groups which are hypersurfaces

Publikováno v: Journal of Algebra. 291(1):72-89

For L a finite non-modular group whose invariants form a polynomial ring and H a subgroup of L containing the derived group of L, Nakajima found necessary and sufficient conditions on H for its invariant ring S H to be a hypersurface. In a crucial st

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Symmetric Powers of Modular Representations for Groups with a Sylow Subgroup of Prime Order

Autor: I.P. Hughes, Gregor Kemper

Publikováno v: Journal of Algebra. 241(2):759-788

Let V be a representation of a finite group G over a field of characteristic p . If p does not divide the group order, then Molien's formula gives the Hilbert series of the invariant ring. In this paper we find a replacement of Molien's formula which

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Depth of modular invariant rings

Autor: David L. Wehlau, R. J. Shank, H. E. A. Campbell, Gregor Kemper, I.P. Hughes

Publikováno v: Scopus-Elsevier

It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation. For modular representations the ring of invariants usually f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d654a29f6e36429a53c28739a81b1dcb
https://doi.org/10.1007/bf01237176

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Some remarks on hilbert functions of veronese algebras

Autor: Gregory G. Smith, H. E. A. Campbell, Anthony V. Geramita, I.P. Hughes, David L. Wehlau

Publikováno v: Communications in Algebra. 28:1487-1496

We study the Hilbert polynomials of finitely generated graded algebras R, with generators not all of degree one (i.e. non-standard). Given an expression P(R,t)=a(t)/(1-tl ) n for the Poincare series of R as a rational function, we study for 0 ≤ i �

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https://doi.org/10.1080/00927870008826908

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Symmetric powers of modular representations, hilbert series and degree bounds

Autor: Gregor Kemper, I.P. Hughes

Publikováno v: Communications in Algebra. 28:2059-2088

Let G = Z p be a cyclic group of prime order p with a representation G → GL(V) over a field K of characteristic p. In 1976, Almkvist and Fossum gave formulas for the decomposition of the symmetric powers of V in the case that V is indecomposable. F

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https://doi.org/10.1080/00927870008826944

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

Autor: H. E. A. Campbell, R. J. Shank, David L. Wehlau, Anthony V. Geramita, I.P. Hughes

Publikováno v: Canadian Mathematical Bulletin. 42:155-161

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 ofmcopies

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https://doi.org/10.4153/cmb-1999-018-4

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2-Dimensional vector invariants of parabolic subgroups of Gl2(Fp) over the field Fp

Autor: I.P. Hughes, H. E. A. Campbell

Publikováno v: Journal of Pure and Applied Algebra. 112:1-12

Given a group G acting on a finite dimensional vector space V over any field k , we ask for the structure of the ring of invariants of the diagonal action of the group on the symmetric algebra of m copies of V , the so-called m -dimensional vector in

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https://doi.org/10.1016/0022-4049(95)00128-x

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Properties of functions associated with invariant theory

Autor: H. E. A. Campbell, R. B. Bell, I.P. Hughes

Publikováno v: Communications in Algebra. 22:381-396

We consider the ring of invariants RG obtained by letting a finite group G act via its regular representation on a polynomial ring with indeterminates over an algebraically closed field of characteristic zero. We note that the Hilbert series of RG ca

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1a278e9dd2846f73ff38613f6121bb00
https://doi.org/10.1080/00927879408824855

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