Newbetuts
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New posts in p-groups
For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.
group-theory
finite-groups
sylow-theory
p-groups
wreath-product
Abelian $p$-group with unique subgroup of index $p$
abstract-algebra
group-theory
finite-groups
p-groups
If $H$ is a proper subgroup of a $p$-group $G$, then $H$ is proper in $N_G(H)$.
abstract-algebra
group-theory
finite-groups
p-groups
Characterizations of the $p$-Prüfer group
abstract-algebra
group-theory
p-groups
Find the upper central series of $Q_{2^n}$.
group-theory
finite-groups
quaternions
group-presentation
p-groups
Part of simple proof of nontrivial center in p-group
group-theory
finite-groups
p-groups
A finite $p$-group cannot be simple unless it has order $p$
abstract-algebra
group-theory
finite-groups
sylow-theory
p-groups
References on the theory of $2$-groups.
group-theory
reference-request
finite-groups
p-groups
2-groups
Proving that if $|G|=p^n$ then $\exists a \in G:|C(a)| = p^{n-1}$
group-theory
p-groups
Understanding the definition of Sylow $p$-subgroups
group-theory
definition
sylow-theory
p-groups
maximal-subgroup
Known bounds for the number of groups of a given order.
group-theory
finite-groups
asymptotics
p-groups
groups-enumeration
Prove, that group of order $p^2$ is abelian.
abstract-algebra
group-theory
abelian-groups
p-groups
All $p$-groups have a normal subgroup of each possible order. [duplicate]
abstract-algebra
group-theory
normal-subgroups
p-groups
Prove that: A group $G$ of order $p^n$ has normal subgroup of order $p^k$, for all $0\le k\le n$.
abstract-algebra
group-theory
normal-subgroups
p-groups
There exists only two groups of order $p^2$ up to isomorphism.
group-theory
finite-groups
p-groups
A $p$-group of order $p^n$ has a normal subgroup of order $p^k$ for each $0\le k \le n$
abstract-algebra
group-theory
finite-groups
p-groups
More than 99% of groups of order less than 2000 are of order 1024?
abstract-algebra
group-theory
finite-groups
p-groups
groups-enumeration
Find the number of subgroups of $\mathbb Z_{p^3} \times \mathbb Z_{p^2}$ [duplicate]
abstract-algebra
group-theory
finite-groups
p-groups
Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
combinatorics
group-theory
finite-groups
group-cohomology
p-groups
Show ${\rm Aut}(G)$ is a $2$-group, where $G$ is given by a particular presentation
group-theory
automorphism-group
group-presentation
p-groups
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