# 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 |
---|---|

Title | Zero-separating invariants for finite groups |

Authors | Elmer, J. and Kohls, M. |

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. |

Language | English |

Publisher | Elsevier |

Journal | Journal of Algebra |

ISSN | 0021-8693 |

Publication dates | |

Online | 13 May 2014 |

Print | 01 Aug 2014 |

Publication process dates | |

Deposited | 15 Apr 2016 |

Submitted | 05 Aug 2013 |

Accepted | 26 Apr 2014 |

Output status | Published |

Digital Object Identifier (DOI) | https://doi.org/10.1016/j.jalgebra.2014.03.044 |

First submitted version |

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