Two-dimensional Vector Invariants Of Finite Two-dimensional Orthogonal Groups Of Plus Type

Suppose p is an odd prime number and F_p is a prime field of characteristic p.Let O₂⁺（Fp）be the two-dimensional orthogonal group of plus type over Fp.We consider the degree-preserving Fp-action of O₂⁺（Fp）on the polynomial ring Fp[2V]=Fp[x1,y1,x2,y2].In this thesis,we find a generating set for the ring of invariants Fp[x1,y1,x2,y2]^O2^+（）Fp,more precisely,we construct invariants N1,N2,u12,B0,...,Bp-1∈Fp[x1,y1,x2,y2]^O2⁺（Fp）such that Fp[x1,y1,x2,y2]^O2⁺（Fp）is generated by{N1,N2,u12,Bk|0≤k≤p-1}.Let H be the Sylow p-subgroup of O₂⁺（Fp）,we also find a generating set for Fp[2V]^Has an Fp[2V]^O2⁺（Fp）-module.