Noether's bound for finite group actions

Add to your list(s) Download to your calendar using vCal

• Pal Hegedus, Central European University
• Wednesday 03 December 2014, 16:30-17:30
• MR12.

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 n^c (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.

This talk is included in these lists:

• Algebra and Representation Theory Seminar
• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.