Lower Degree Bounds for
نویسنده
چکیده
We prove two statements. The rst one is a conjecture of Ian Hughes which states that if f1; : : : ; fn are primary invariants of a nite linear group G, then the least common multiple of the degrees of the fi is a multiple of the exponent of G. The second statement is about vector invariants: If G is a permutation group and K a eld of positive characteristic p such that p divides jGj, then the invariant ring KV m ] G 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 which is independent of the representation.
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