University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > Noether's bound for finite group actions

Noether's bound for finite group actions

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  • UserPal Hegedus, Central European University
  • ClockWednesday 03 December 2014, 16:30-17:30
  • HouseMR12.

If you have a question about this talk, please contact David Stewart.

Let a finite group G act on a K-vector space V. Then it also acts on the algebra of polynomials K[V]. Emmy Noether proved first that the ring of polynomial invariants K[V]G is finitely generated and if char(K)=0 then the invariant polynomials of degree at most |G| generate. The bound is sharp for cyclic groups but in the non-cyclic case several improvements exist. In particular, Cziszter and Domokos proved that the invariants of degree at most |G|/2 generate unless G has a cyclic subgroup of index at most 2 or G is from a list of four counterexamples. In this talk I describe a joint result with Laci Pyber: there exists an absolute constant c such that if the invariants of degree at most |G|/n do not generate the ring of invariants then G has a cyclic subgroup of index nc (if G is solvable) or a cyclic subgroup of index n(c logn) (for arbitrary G).

This talk is part of the Algebra and Representation Theory Seminar series.

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