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SUMMARY:Noether's bound for finite group actions - Pal Hegedus\, Central E
 uropean University
DTSTART:20141203T163000Z
DTEND:20141203T173000Z
UID:TALK54681@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:Let a finite group G act on a K-vector space V. Then it also a
 cts 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 bou
 nd is sharp for cyclic groups but in the non-cyclic case several improveme
 nts 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 desc
 ribe a joint result with Laci Pyber: there exists an absolute constant c s
 uch that if the invariants of degree at most |G|/n do not generate the rin
 g of invariants then G has a cyclic subgroup of index n^c^ (if G is solvab
 le) or a cyclic subgroup of index n^(c logn)^ (for arbitrary G).
LOCATION:MR12
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