The Invariants Of Three Kinds Of Finite Irreducible Groups Generated By Reflections Over Finite Fields

The classifications of finite irreducible real and complex reflection groups have beencompleted, and reflection groups over finite fields (Char≠2)have also been classified.Since it is very effective to classify groups by means of invariants, many mathematiciandevote themselves to invariant theory. We know that the invariants of finite irreduciblereal and complex reflection groups have been worked out. In this paper, we mainlyconsider the invariants of three kinds of finite irreducible reflection groups over finitefields.The concrete contents of this thesis are listed as follows:In introduction, we review the history and development of finite reflection groups,and introduce the latest results of invariant thoery related to finite reflection groups.In chapter 1, we introduce some essential definitions and preliminary theorems re-lated to this thesis, and quote the results of classifications of finite irreducible reflectiongroups over real number field and over finite fields.In Chapter 2, we introduce the invariants of all kinds of finite irreducible real reflectiongroups.In Chapter 3, we study the invariants of three kinds of finite irreducible groups,A_n~p(p(?)(n+1)), B_n~p(n≥2), D_n~p(n≥4), generated by reflections and compute the primitiveinvariants of them. Moreover, we can determinate all the invariants of them.