PSL(2,5) is isomorphic to A5
From Groupprops
This article gives a proof/explanation of the equivalence of multiple definitions for the term alternating group:A5
View a complete list of pages giving proofs of equivalence of definitions
Statement
The projective special linear group of degree two over field:F5, which we denote , is isomorphic to alternating group:A5.
Facts used
-
has order
-
has order
by order formulas for linear groups of degree two
- A5 is the unique simple non-abelian group of smallest order: This says that
is the simple non-abelian group of smallest possible order and also that any simple non-abelian group of the same order as
must be isomorphic to
.
- Projective special linear groups are simple with some exceptions, but
is not among the exceptions, so
is simple.
Proof
The proof follows directly by combining Facts (1)-(4).