New posts in nilpotent-groups

If $G$ is a nilpotent group and $H\leq G$ with $H[G,G]=G$ then $H=G$.

If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic? [duplicate]

Prove that in a nilpotent group every normal subgroup of prime order is contained in the center.

Nonabelian infinite nilpotent groups

If a nilpotent group has an element of prime order $p$, so does its centre.

Why is the direct product of a finite number of nilpotent groups nilpotent?

Characterization of nilpotency with normal subgroups

A question about Frattini subgroup of specific form

Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.

Prove Fitting's theorem for finite groups

If $G / Z(G)$ nilpotent then G is nilpotent.

If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$ [closed]

If $N$ is normal in $G$, show $Z_{i}(G)N/N \leq Z_{i}(G/N)$ where $Z_{i}(G)$ is the $i$th term in the upper central series for $G$.