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.