# PSL(2,3) is isomorphic to A4

From Groupprops

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

- PGL(2,3) is isomorphic to S4
- is a subgroup of index two in for odd (see order formulas for linear groups of degree two)
- is the
*unique*subgroup of index two in (see subgroup structure of symmetric group:S4)

## Proof

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