# Zero-separating invariants for finite groups

Article

Elmer, J. and Kohls, M. 2014. Zero-separating invariants for finite groups. Journal of Algebra. 411, pp. 92-113. https://doi.org/10.1016/j.jalgebra.2014.03.044
Type Article Zero-separating invariants for finite groups Elmer, J. and Kohls, M. 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. English Elsevier Journal of Algebra 0021-8693 13 May 2014 01 Aug 2014 15 Apr 2016 05 Aug 2013 26 Apr 2014 Published https://doi.org/10.1016/j.jalgebra.2014.03.044 ElmerKohlsSigmaDelta.pdf

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