Normal subgroup of finite index
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: [[conjunction involving::normal subgroup]][[defining ingredient::normal subgroup| ]] and [[conjunction involving::subgroup of finite index]][[defining ingredient::subgroup of finite index| ]]
View other subgroup property conjunctions | view all subgroup properties
Definition
Symbol-free definition
A normal subgroup of finite index in a group is a subgroup satisfying the following equivalent conditions:
- It is normal and its index in the whole group is finite
- It is the kernel of a homomorphism to a finite group
- It is the normal core of a subgroup of finite index