Quiz:Splitting field
From Groupprops
Rational and ambivalent
An ambivalent group is a group in which every element is conjugate to its inverse. For a finite group, this is equivalent to every character in characteristic zero being real-valued.
A rational group is a group in which any two elements generating the same cyclic subgroup are conjugate. For a finite group, this is equivalent to every character in characteristic zero being rational-valued.
Splitting fields in characteristic zero
Rings of realization