# Tagged Questions

**1**

vote

**0**answers

70 views

### Galois correspondence for action of general linear group on purely transcendental extension

For a fixed positive integer $n$, the group $G=GL_n(\mathbb{C})$ acts on the field $K=\mathbb{C}(t_1,\ldots,t_n)$ by linear change of variables. I would like to know if there is something like a ...

**0**

votes

**0**answers

27 views

### The invariant field for the dual of the augmentation lattice

Let $G$ be some finite group and $J_G$ be $ZG$ modulo the ideal $\{n\sum_{g} g | n\in\mathbb N\}$, or equivalently the dual of the augmentation ideal which is the kernel of $ZG\to Z$ sending $g$ to ...

**9**

votes

**2**answers

515 views

### On the field of invariants of a finite group

So let $G$ be a finite group and let $\iota:G\rightarrow S_n$ be an embedding of $G$ in a symmetric group of degree $n$ for some fixed integer $n$. Let $K$ be a fixed field of characteristic $0$. The ...