Just infinite group

Symbol-free definition
A group is said to be just infinite if it satisfies the following equivalent conditions:


 * 1) It is infinite and every nontrivial normal subgroup is of finite index, i.e., is a defining ingredient::normal subgroup of finite index.
 * 2) It is infinite and every proper quotient is finite.
 * 3) It is infinite and every subgroup of infinite index is a defining ingredient::core-free subgroup, i.e., the normal core of any subgroup of infinite index is trivial.

Examples

 * The group of integers is a just infinite group.
 * Any infinite simple group is a just infinite group.