Reference or idea of a proof (on A-groups) There is the following result on wiki:

The Fitting subgroup of a solvable $A$-group is equal to the direct product of the centers of the terms of the derived series.

An $A$-group is a (finite) group whose all Sylow subgroup are abelian. The proof of this result can be found on Huppert 1967. Unfortunally I don't have access to the book and I cannot read German.
So, does anyone know another reference or how to prove?

The proofs use the theory of system normalizers in solvable groups.
These results were proved originally in
D. Taunt, On $A$-groups, Cambridge Phil. Soc. 45, 14-42, 1949,
which is in English.
