Finite quotient of a group
= Finite quotient of a group
= Finite quotients of a group
{synonym}
A finite quotient is the image of a <group> under a surjective <group homomorphism> to a <finite group>. A group has no nontrivial finite quotients exactly when every homomorphism from it to a finite group is trivial. This property does not prohibit finite or finite-quotient-bearing subgroups.