Zero-separating invariants for finite groups
Elmer, Jonathan ORCID: https://orcid.org/0000-0001-5296-1987 and Kohls, Martin
(2014)
Zero-separating invariants for finite groups.
Journal of Algebra, 411
.
pp. 92-113.
ISSN 0021-8693
[Article]
(doi:10.1016/j.jalgebra.2014.03.044)
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Abstract
We fix a field k of characteristic p. For a finite group G denote by δ(G) and σ(G) respectively the minimal number d, such that for every finite dimensional representation V of G over k and every v ∈ V^G \ {0} or v ∈ V \ {0} respectively, there exists a homogeneous invariant f of positive degree at most d such that f(v) = 0. Let P be a Sylow-p-subgroup of G (which we take to be trivial if the group order is not divisble by p). We show that δ(G) = |P|. If N_G(P)/P is cyclic, we show σ(G) ≥ |N_G(P)|. If G is p-nilpotent and P is not normal in G, we show σ(G) ≤ |G|/l , where l is the smallest prime divisor of |G|. These results extend known results in the non-modular case to the modular case.
Item Type: | Article |
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Research Areas: | A. > School of Science and Technology > Design Engineering and Mathematics |
Item ID: | 19313 |
Useful Links: | |
Depositing User: | Jonathan Elmer |
Date Deposited: | 15 Apr 2016 10:28 |
Last Modified: | 07 Jun 2022 19:37 |
URI: | https://eprints.mdx.ac.uk/id/eprint/19313 |
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