On the Invariants of Root Subgroups of Finite Classical Groups

Abstract

We show that the invariant fields F _q (X ₁ , . . . ,X _n ) ^G are purely transcendental over F _q 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 Poincaré series are presented.