洪有情黃文彬2019-09-052003-6-192019-09-052003http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22N2003000135%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101870Let Q be a nondegenerate quadratic form over the nite eld Fq of odd prime power order q with charFq 6= 2 and Let On(Fq) be the associated orthogonal group. Let On(Fq) act linearly on the polynomial ring Fq[x1; : : : ; xn]: In this thesis we nd the invariant subring Fq[x1; x2; x3; x4; x5]O5(Fq ) with explicit generators. We also prove that this subring is a UFD.