PSL(2,3) is isomorphic to A4

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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).