New posts in p-groups

For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.

Abelian $p$-group with unique subgroup of index $p$

If $H$ is a proper subgroup of a $p$-group $G$, then $H$ is proper in $N_G(H)$.

Characterizations of the $p$-Prüfer group

Find the upper central series of $Q_{2^n}$.

Part of simple proof of nontrivial center in p-group

A finite $p$-group cannot be simple unless it has order $p$

References on the theory of $2$-groups.

Proving that if $|G|=p^n$ then $\exists a \in G:|C(a)| = p^{n-1}$

Understanding the definition of Sylow $p$-subgroups

Known bounds for the number of groups of a given order.

Prove, that group of order $p^2$ is abelian.

All $p$-groups have a normal subgroup of each possible order. [duplicate]

Prove that: A group $G$ of order $p^n$ has normal subgroup of order $p^k$, for all $0\le k\le n$.

There exists only two groups of order $p^2$ up to isomorphism.

A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$

More than 99% of groups of order less than 2000 are of order 1024?

Find the number of subgroups of $\mathbb Z_{p^3} \times \mathbb Z_{p^2}$ [duplicate]

Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?

Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation