Rational invariants of certain classical similitude groups over finite fields Nan JizhuChen Yin 12F2020G40rational invariantrational function fieldorthogonal similitude groupunitary similitude group Let $F_q$ be a finite field with $\Char F_q\neq2$ and $F_q(X_1,\dots,X_n)$ be a rational function field. In the present paper, we construct explicit transcendental bases of the invariant subfields of orthogonal similitude and unitary similitude groups on $F_q(X_1,\dots,X_n)$ over $F_q$. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3330 10.1512/iumj.2008.57.3330 en Indiana Univ. Math. J. 57 (2008) 1947 - 1958 state-of-the-art mathematics http://iumj.org/access/