Zero-separating invariants for finite groups

Jonathan Elmer, Martin Kohls*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Early online date13 May 2014
Publication statusPublished - 1 Aug 2014

Bibliographical note

This paper was prepared during visits of the first author to TU München and the second author to University of Aberdeen. The second of these visits was supported by the Edinburgh Mathematical Society's Research Support Fund. We want to thank Gregor Kemper and the Edinburgh Mathematical Society for making these visits possible. We also thank K. Cziszter for some helpful communication via eMail, and the anonymous referee for useful suggestions.


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