Galois Solvable Group and Realizability over \mathbb{Q} for |G|=p^n

[Kummer]

Galois Group

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

 

[mathwonk]

i think so. arent all solvable groups known to be galois groups? what did shafarevich prove?

http://www.math.uiuc.edu/Algebraic-Number-Theory/0136/

 

[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)).

 

[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.

 

[matt grime]

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)).

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?

 

[Kummer]

Is it solved for abelian extensions?