On the invariants of root subgroups of finite classical groups - Jizhu Nan; Yufang Qin (Український математичний журнал, 2013)
We show that invariant fields Fq(X1, . . . , Xn)G are purely transcendental over Fq if G are root subgroups of finite classical groups. The key step is to find good similar groups of our groups. Moreover, the invariant rings of the root subgroups of special linear groups are shown to be polynomial rings, and their corresponding Poincare series are presented.