The Transfer Ideal Under The Action Of U_6p In The Modular Case

The representation of a finite group can be divided into modular representation and ordinary representation according to the relationship between the order of the group G and the characteristic of the field IF.There is a great difference between modular representation and ordinary representation in the study of invariants.In the case of the ordinary representation,the invariant ring is a polynomial ring if and only if the group is generated by pseudoreflection,which is not necessarily under the modular representation.The invariant ring of a finite group is C-M under the ordinary representation,but it is not necessarily true under the modular representation.That is,invariant problem of a special form that is true under the ordinary representation is often not true under the modular representation.This paper mainly studies the modular representation of the finite group U6p and the structure of Transfer ideal Im(TrU6p)under this representation.In the case of modular representation,the Transfer homomorphic image Im(TrG)is a nontrivial proper ideal of the invariant ring IF[V]G.Therefore,we can use the height of Im(TrG)in the invariant ring F[V]G to measure the structure between the Im(TrG)and the invariant ring F[V]G.This paper first calculates the height of the Transfer ideal Im(TrU6p)in the invariant ring F[V]U6p.Then the coinvariant is used to calculate the specific structure of the Transfer ideal Im(TrU6p).The full paper consists of three parts:The first chapter briefly introduces the basic situation of algebra and the research background of invariant theory and Transfer ideal.The second chapter introduces the definition that this paper mainly involves.In the third chapter,we give the height and structure of the Transfer ideal Im(TrU6p)of the finite group U6p in the case of modular representation.