# Projective special linear group of degree two is ambivalent iff -1 is a square

From Groupprops

## Statement

Suppose is a field and is the Projective special linear group (?) of degree two over . Then, is an Ambivalent group (?) if and only if is a square in .

In particular, when is a finite field with elements, this is equivalent to saying that is an ambivalent group if and only if is a power of or .