Suppose p is an odd prime number and Fp 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. |