Invariant Gorenstein Rings On 3 Dimensional Spaces

This is my master thesis, under the supervision of Professor Amiram Braun. We classify in these paper the Gorenstein invariant rings in the modular case, where the group that acts on the 3-variable polynomial ring is finite , and the Char (F)=p divides the order of this group. We divide our work into several cases that discuss all the situations of the G-module V, where V=span{x,y,z} is the space of the polynomial ring of three coefficients.