# Special unitary group of degree two equals special linear group of degree two over a finite field

From Groupprops

## Statement

Suppose is a prime power. Denote by the special unitary group corresponding to the quadratic extension of the finite field . In particular, is the intersection of with . Then, is isomorphic to the special linear group of degree two . Moreover, if we view both and as subgroups inside , they are conjugate subgroups.