It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow
2
2
-subgroup. This result is generalized for Sylow
p
p
-subgroups, for any prime number
p
p
, while assuming the group to be
p
p
-solvable. In particular, it is proved that a
p
p
-solvable group has a normal Sylow
p
p
-subgroup if
p
p
does not divide the degree of any irreducible character of the group fixed by a field automorphism of order
p
p
.