Feit–Thompson theorem
= Feit–Thompson theorem
{c}
= Odd order theorem
{synonym}
Every finite <group> of odd order is a <solvable group>. In particular, a nonabelian <simple group> has even order and therefore has an <involution> by <Cauchy's theorem for finite groups>. This is a deep theorem, not an elementary consequence of the <Sylow theorems>.