Normal subgroup of least prime order

Definition

A subgroup of a finite group is termed a normal subgroup of least prime order if it is normal and its order is the smallest prime number dividing the order of the group.

Any such subgroup must necessarily be a central subgroup. For full proof, refer: Normal of least prime order implies central

Relation with other properties

Weaker properties

• Central subgroup: For full proof, refer: Normal of least prime order implies central