Simplicity of alternating groups
= Simplicity of alternating groups
{c}
The alternating group $A_n$ is simple for every $n\geq5$. In particular it has no proper subgroup of index two, since every index-two subgroup is normal.
= Simplicity of alternating groups
{c}
The alternating group $A_n$ is simple for every $n\geq5$. In particular it has no proper subgroup of index two, since every index-two subgroup is normal.