### Abstract

Assume a fixed point v∈V^{G} can be separated from zero by a homogeneous invariant f∈k[V]^{G} of degree p^{r}d, where p>0 is the characteristic of the ground field k and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree p^{r}, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power.

Original language | English |
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Pages (from-to) | 371-376 |

Number of pages | 6 |

Journal | Communications in Algebra |

Volume | 45 |

Issue number | 1 |

Early online date | 11 Oct 2016 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- geometrically reductive
- invariant theory
- linear algebraic groups
- prime characteristic

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Elmer, J., & Kohls, M. (2017). On separating a fixed point from zero by invariants.

*Communications in Algebra*,*45*(1), 371-376. https://doi.org/10.1080/00927872.2016.1175465