A CONSTRUCTIVE APPROACH TO NOETHER PROBLEM

A general method is developed to attack Noether's Problem constructive ly by trying to find minimal bases consisting of rational invariants w hich are quotients of polynomials of small degrees. This approach turn s out to be successful for many small groups and for most of the class ical groups with their natural representations. The applications inclu de affirmative answers to Noether's Problem for the conformal symplect ic groups CSp(2n)(q), for the simple subgroups Omega(n)(q) of the orth ogonal groups for n and q odd, for some other subgroups of orthogonal groups and for the special unitary groups SUn(q(2)).