The Transfer Ideal Of Invariant Ring F_p[V]^D_2p Of Dihedral Group D_2pin The Modular Case

In this paper, we firstly introduce some basic concepts and properties of invariants of finite groups. Then we describe the Transfer ideal of invariant ring Fp[V]D2p of dihedral group D2p in the modular case by finding the element of order p, Transfer variety, Hilbert’s Nullstellensatz, and we obtain the radical ideal of Transfer ideal of Fp[V]D2p and the Transfer ideal of Fp[V]D2p.The main structure of this paper are as follows:Chapter1is an introduction, in which we give a brief description of invariant theory of finite groups and the development of Transfer ideal theory.In chapter2, we introduce some basic definitions, properties and theorems needed in this paper.In chapter3, consider the given modular representation of D2p, we get the Transfer variety and the element of order p in D2p. Then we obtain the radical ideal of Transfer ideal of Fp[V]D2p by Hilbert’s Nullstellensatz. In addition, we obtain the Transfer ideal of Fp[V]D2p.