Powering-invariant and normal not implies quotient-powering-invariant
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., powering-invariant normal subgroup) need not satisfy the second subgroup property (i.e., quotient-powering-invariant subgroup)
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EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property powering-invariant normal subgroup but not quotient-powering-invariant subgroup|View examples of subgroups satisfying property powering-invariant normal subgroup and quotient-powering-invariant subgroup
It is possible to have a group and a powering-invariant normal subgroup of that is not quotient-powering-invariant: in other words, is a normal subgroup of that is also a powering-invariant subgroup of , but there exists a prime number such that is -powered and is not -powered.