Group in which every nontrivial normal subgroup has finite index

Definition
A group in which every nontrivial normal subgroup has finite index is a group with the property that every nontrivial normal subgroup (i.e., every defining ingredient::normal subgroup other than the trivial subgroup) is a defining ingredient::subgroup of finite index: in other words, its index in the whole group is finite.

Facts

 * Margulis' normal subgroup theorem
 * Burger-Mozes normal subgroup theorem