# Quiz:Splitting field

## 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