Normal subgroup of least prime order: Difference between revisions
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Latest revision as of 23:57, 7 May 2008
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