## Abstract

We prove two statements. The first one is a conjecture of Ian Hughes which states that if f_{1}, . . . , f_{n} are primary invariants of a finite linear group G, then the least common multiple of the degrees of the f_{i} is a multiple of the exponent of G. The second statement is about vector invariants: If G is a permutation group and K a field of positive characteristic p such that p divides |G|, then the invariant ring K[V^{m}] of m copies of the permutation module V over K requires a generator of degree m(p - 1). This improves a bound given by Richman [6], and implies that there exists no degree bound for the invariants of G that is independent of the representation.

Original language | English |
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Pages (from-to) | 135-144 |

Number of pages | 10 |

Journal | Transformation Groups |

Volume | 3 |

Issue number | 2 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |