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If $G$ is a nilpotent group and $H\leq G$ with $H[G,G]=G$ then $H=G$.
group-theory
nilpotent-groups
derived-subgroup
If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic? [duplicate]
group-theory
nilpotent-groups
derived-subgroup
Can a group have a cyclical derived series?
abstract-algebra
group-theory
infinite-groups
derived-subgroup
Any Subgroup containing commutator subgroup is normal.
abstract-algebra
group-theory
normal-subgroups
derived-subgroup
Commutator subgroup $G'$ is a characteristic subgroup of $G$
abstract-algebra
group-theory
characteristic-subgroups
derived-subgroup
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