Group of prime-sixth or higher order contains abelian normal subgroup of prime-fourth order for prime equal to two
Any group of order contains an Abelian normal subgroup (?) (hence, Abelian normal subgroup of group of prime power order (?)) of order . In other words, for the prime , any group of order contains an abelian normal subgroup of order .
- Existence of abelian normal subgroups of small prime power order: This states that if , then any finite -group of order has an abelian normal subgroup of order . Note that our result does not follow from this because the needed for is .
- Abelian-to-normal replacement theorem for prime-cube order
- Abelian-to-normal replacement theorem for prime-fourth order