Let F be any field. Let G be any reductive linear algebraic group and consider a finite dimensional rational representation V of G. Then the Falgebra F[V ] of polynomial invariants for G acting on V is finitely generated. The Noether Number β(G, V ) is the highest degree of an element of a minimal homogeneous generating set for F[V ]. We survey what is known about Noether Numbers, in particular describing various upper and lower bounds for them. Both finite and infinite groups and both… CONTINUE READING