Every normal subgroup of a powerful odd p-group contained in G^p is powerfully nilpotent, with an analogous statement for p=2 inside G^4.
González-Sánchez and A
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Normal Subgroups of Powerful $p$ -groups
Every normal subgroup of a powerful odd p-group contained in G^p is powerfully nilpotent, with an analogous statement for p=2 inside G^4.