On Rings of Invariants of Finite Linear Groups

Publisher Summary This chapter discusses the rings of invariants of finite linear groups. Let τ be a field. An element τ of finite order in GLn(k) is called a pseudo-reflection if rank(τ − I) = 1. A finite subgroup of GLn(k) is called small if it contains no pseudo-reflection. The chapter discusses a few basic properties of the fundamental groups of Noetherian normal domains. The chapter presents the assumption that R is a Noetherian normal domain of which k is the quotient field and Ks is the fixed separable closure of k. Also, L is a finite extension of K, and S is the integral closure of R in L. Then, S is a 1-unramified extension of R if every prime ideal of height 1 in S is unramified over R.