Zero-separating invariants for finite groups

Jonathan Elmer, Martin Kohls*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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∈VG{0} or v∈V{0} respectively, there exists a homogeneous invariant f∈k[V]G 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 divisible 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.

Original languageEnglish
Pages (from-to)92-113
Number of pages22
JournalJournal of Algebra
Volume411
Early online date13 May 2014
DOIs
Publication statusPublished - 1 Aug 2014

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