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New posts in nilpotent-groups
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
Prove that in a nilpotent group every normal subgroup of prime order is contained in the center.
abstract-algebra
group-theory
normal-subgroups
nilpotent-groups
Nonabelian infinite nilpotent groups
group-theory
examples-counterexamples
infinite-groups
nilpotent-groups
If a nilpotent group has an element of prime order $p$, so does its centre.
group-theory
normal-subgroups
nilpotent-groups
Why is the direct product of a finite number of nilpotent groups nilpotent?
group-theory
direct-product
nilpotent-groups
Characterization of nilpotency with normal subgroups
group-theory
finite-groups
normal-subgroups
nilpotent-groups
A question about Frattini subgroup of specific form
abstract-algebra
group-theory
finite-groups
nilpotent-groups
frattini-subgroup
Show $G=\langle\delta\rangle\ltimes D$ is nilpotent of class $2$.
group-theory
abelian-groups
semidirect-product
nilpotent-groups
Prove Fitting's theorem for finite groups
group-theory
finite-groups
normal-subgroups
nilpotent-groups
If $G / Z(G)$ nilpotent then G is nilpotent.
abstract-algebra
group-theory
nilpotent-groups
If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$ [closed]
abstract-algebra
group-theory
normal-subgroups
nilpotent-groups
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 $G$.
abstract-algebra
group-theory
normal-subgroups
nilpotent-groups
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