### Abstract

Let F_{q} be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of F_{q} -automorphisms acting linearly on the rational function field F_{q}(x_{1}, …, x_{n}). We shall prove that the invariant subfield F_{q}(x_{1},…, x_{n})^{O(n, Q)} is a purely transcendental extension over F_{q} for n = 5 by giving a set of generators for it.

Original language | English |
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Pages (from-to) | 313-319 |

Number of pages | 7 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 48 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 Jan 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Chiang, L., & Hung, Y. C. (1993). The invariants of orthogonal group actions.

*Bulletin of the Australian Mathematical Society*,*48*(2), 313-319. https://doi.org/10.1017/S0004972700015720