Zero-separating invariants for finite groups

Elmer, Jonathan and Kohls, Martin (2014) Zero-separating invariants for finite groups. Journal of Algebra, 411 (1). pp. 92-113. ISSN 0021-8693

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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
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19313
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Depositing User: Jonathan Elmer
Date Deposited: 15 Apr 2016 10:28
Last Modified: 03 Apr 2019 18:20

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