# Projective special linear group of degree two has a class-inverting automorphism

From Groupprops

## Statement

Let be a field and be the Projective special linear group (?) of degree two over . Then, is a Group having a class-inverting automorphism (?). In other words, there is an automorphism of that is a Class-inverting automorphism (?): it sends every element into the conjugacy class of its inverse.

## Facts used

- Special linear group of degree two has a class-inverting automorphism
- Class-inverting automorphism induces class-inverting automorphism on any quotient

## Proof

The proof follows directly from facts (1) and (2).