Show that $G$ is nilpotent when the quotient group is nilpotent
45310
If $H\leq Z (G)$ and $G/H$ is nilpotent, then $G$ is nilpotent.
146760
Prove that H is a subgroup of G
11003
Proving that $G/N$ is an abelian group
29003
Is the dihedral group $D_n$ nilpotent? solvable?
123610
How to show that the commutator subgroup is a normal subgroup
133019
Nilpotent elements in $\mathbb Z_n$
156319
Show that a group with $|G| = 33$ contains an element of order $3$
15904
Prime ideal and nilpotent elements
60208
Proof of property of abelian group
154398
Show that H is a subgroup of G
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
114221
A Group $G$ is soluble $\iff G^{(k)}=\{e\}$ for some $k$
132280
Let $G$ be a group of order 35. Show that $G \cong Z_{35}$
103216
The set $\{g^2 | g \in G\}$ in a group $G$
63780
to show characteristic subgroup is normal in G
150854
Identifying a quotient group (NBHM-$2014$)