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