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From Diffgeom

The article on this topic in the Group Properties Wiki can be found at: normal subgroupTemplate:Subgroup property

Contents 1 Definition 2 Facts 2.1 Normal subgroup and quotient goup 2.2 Normal subgroups of the fundamental group 2.3 Normal subgroups of the structure group

Definition

A subgroup H of a group G is termed normal if it satisfies the following equivalent conditions:

• H is the kernel of a homomorphism from G, i.e. there is a homomorphism of groups such that φ ^{− 1}(e) = H
• , or in other words, for all
• xHx ^{− 1} = H

Facts

Normal subgroup and quotient goup

Normal subgroups of the fundamental group

Normal subgroups of the structure group