List questions from nilpotent-groups

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question on nilpotent group.

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central series for a finite $p$-group

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List Question

Free nilpotent group on 2 generators of class 2.

Conjugacy classes in virtually nilpotent groups

Proving a necessary and sufficient condition for a finite group being nilpotent

A commutator with an element of finite order in a nilpotent group

Is the dihedral group $D_n$ nilpotent? solvable?

Join of finitely many nilpotent subgroups (+ additional properties) is nilpotent?

Does every two-generated subgroups being nilpotent imply that the group itself is nilpotent?

question on nilpotent group.

Equivalence of Nilpotence in group

If $G=\langle\{a_i\}_{i=1}^r\rangle$ is nilpotent with $|a_i|=m_i$, show that $|G|$ divides a power of $\prod_{i=1}^rm_i$ and is finite.

Generalization of a property of finite nilpotent groups

Equivalent condition for finite Nilpotent group

Nilpotent Group G

If $G$ nilpotent and $G/G'$ is cyclic then $G'=1$.

central series for a finite $p$-group

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