PSL(2,3) is isomorphic to A4

This article gives a proof/explanation of the equivalence of multiple definitions for the term alternating group:A4
View a complete list of pages giving proofs of equivalence of definitions

Statement

The projective special linear group of degree two over field:F3 is isomorphic to alternating group:A4.

Facts used

1. PGL(2,3) is isomorphic to S4
2. $PSL(2,q)$ is a subgroup of index two in $PGL(2,q)$ for $q$ odd (see order formulas for linear groups of degree two)
3. $A_{4}$ is the unique subgroup of index two in $S_{4}$ (see subgroup structure of symmetric group:S4)

Proof

The proof follows directly by combining Facts (1), (2), and (3).