# Galois Solvable Group

1. Aug 19, 2007

### Kummer

Galois Group

Is $$G$$ realizable over $$\mathbb{Q}$$ given that $$|G|=p^n$$ ?

Last edited: Aug 19, 2007
2. Sep 8, 2007

3. Sep 8, 2007

### Kummer

Is it possible to have this in pdf? Thank you.

(Note: Shafarevich's theorem and work will be worthless if the Inverse Galois Problem is true. (Unless it depends breaking the group into solvable groups first)).

4. Sep 8, 2007

### mathwonk

your note strikes me as odd. i would say shafarevich's work is more accurately described as the best work so far toward the inverse galois problem.

see the book of serre, topics in galois theory.

Last edited: Sep 8, 2007
5. Sep 9, 2007

### matt grime

Get a (free) ps viewer, or run ps2pdf (standard *nix program, and installed if you have LaTeX on Win).

Your last comment seems to be yet another of your over-arching and dismissive comments about mathematics. These are strange since you seem to know a lot of number theory. How can you dismiss this work as being worthlesss if IGP is true? Surely you must then think all mathematics is worthless if it doesn't prove absolutely everything simultaneously?

6. Sep 10, 2007

### Kummer

Is it solved for abelian extensions?