Shafarevich’s theorem

Theorem (Shafarevich’s Theorem).

Every finite solvable group occurs as a Galois group of a finite extension of $\mathbb{Q}$.

One can find a proof in [S-W].

References

• S-W Alexander Schmidt and Kay Wingberg, http://www.math.uiuc.edu/Algebraic-Number-Theory/0136/Shafarevich’s Theorem on Solvable Groups as Galois Groups.
Title Shafarevich’s theorem ShafarevichsTheorem 2013-03-22 15:01:17 2013-03-22 15:01:17 alozano (2414) alozano (2414) 8 alozano (2414) Theorem msc 11R32 InverseGaloisProblem Solvable