# Tagged Questions

19 views

113 views

### What can be said about the Galois group of $f(g(x))$?

Supposing we know the Galois groups of $f(x)$ and $g(x)$ over $K$, what can be said about the Galois group of $f(g(x))$? I suppose we can restrict the question to normal polynomials over ...
29 views

### How to prove that there are at least two different unital homomorphisms for field $K\rightarrow K$

How to prove that exists a field K such that there are two unital homomorphisms between fields $f:K\rightarrow K$? Homomorphism is unital if $f(1) = 1$
86 views

### Closure of Normal Subgroups of the Galois Group for an Infinite Galois Extension is Normal

Let K/F be an infinite Galois extension, and let N be a normal sub-group of Gal(K/F). Show that N closure is a normal subgroup of Gal(K/F).
2k views

### What kind of work do modern day algebraists do?

Often times in my studies I get the impression that algebra is just a tool to help with other branches of mathematics, like algebraic geometry, algebraic number theory, algebraic topology, etc. How ...
For even ordered Latin squares, we can create squares in which every cell participates in a $2\times 2$ subsquare by using a simple circulant as for $n=6$ below: ...
### Is there a necessary and sufficient condition to determine the generators of $\mathbb{Z}_p^\times$?
This is something I was wondering about. I know that the generators of the cyclic groups $(\mathbb{Z}_n,+)$ are precisely those integers coprime to $n$, and there are $\phi(n)$ of them. Now the ...