Image of a Normal Subgroup Under a Surjective Homomorphism is a Normal Subgroup

2 Inverse image of a subgroup under a homomorphism is a subgroup.

The image of a subgroup under any homomorphism of groups is again a subgroup.

Image of a Normal Subgroup Under a Surjective Homomorphism is a Normal Subgroup

The centre of a group is a normal subgroup of that group.

A related concept is that of a distinguished subgroup.

The smallest simple non-abelian group is alternating group:A5.

This distinguished group prayed with a middle school delegation.

The intersection of arbitrarily many subgroups is a subgroup.

Intersection of two normal subgroups is a normal subgroup.

Any subgroup of an abelian group is normal, and hence factor groups can be formed freely.

Any subgroup of an abelian group is normal, and hence factor groups can be formed freely.

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Simple group — In mathematics, a simple group is a group which is not the trivial group and whose only normal subgroups are the trivial group and the group itself.

Paul VI to a group of Buddhist Leaders, June 15, 1977: “To the distinguished group of Buddhist leaders from Japan we bid a warm welcome.