Questions:Normal subgroup

This is a questions page on normal subgroup, listing common questions that may occur both to people encountering the definition for the first time and to people who have spent some time with the definition.

In addition to reading these questions, you should read: normal subgroup (the main page on the topic), nonstandard definitions of normal subgroup, proving normality, using normality, normal versus characteristic, ubiquity of normality.

Also see facts about normality, facts that prove that a subgroup is normal, and facts that use that a subgroup is normal.