PGL(2,5) is isomorphic to S5

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This article gives a proof/explanation of the equivalence of multiple definitions for the term symmetric group:S5
View a complete list of pages giving proofs of equivalence of definitions

Statement

The projective general linear group of degree two over field:F5, denoted PGL(2,5), is isomorphic to symmetric group:S5.

Related facts

Similar facts

Facts used

  1. PSL(2,5) is isomorphic to A5
  2. S_5 is the automorphism group of A_5
  3. PGL(2,p) is the automorphism group of PSL(2,p) for any prime p

Proof

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