Lower degree bounds for modular invariants and a question of I. Hughes

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Abstract

We prove two statements. The first one is a conjecture of Ian Hughes which states that if f1, . . . , fn are primary invariants of a finite 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 field of positive characteristic p such that p divides |G|, then the invariant ring K[Vm] 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 languageEnglish
Pages (from-to)135-144
Number of pages10
JournalTransformation Groups
Volume3
Issue number2
DOIs
StatePublished - 1998
Externally publishedYes

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