Let F_q be a finite field of characteristic p, K a field containing it, and R = K[X_1,..., X_n] a polynomial ring in n variables. The general linear group GL_n(F_q) has a natural action on R by degree preserving ring automorphisms. L. E. Dickson showed that the subring of elements which are fixed by this group action is a polynomial ring [Di], though for an arbitrary subgroup G of GL_n(F_q), the structure of the ring of invariants R~G may be rather mysterious.
展开▼
机译：令F_q为特征p的有限域，K为包含它的域，R = K [X_1，...，X_n]为n个变量的多项式环。通用线性基团GL_n（F_q）通过保持环的自同构度而对R具有自然作用。 L. E. Dickson表明，通过该组动作固定的元素的子环是多项式环[Di]，尽管对于GL_n（F_q）的任意子组G，不变环R〜G的环结构可能相当神秘。
展开▼
