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New posts in p-groups
Non-abelian $p$-group; abelian subgroups of index $p$
group-theory
finite-groups
p-groups
Which $p$-groups can be Sylow p-subgroups with trivial intersection?
group-theory
finite-groups
p-groups
Understanding the normalizer of a Sylow $p$-subgroup
abstract-algebra
group-theory
sylow-theory
p-groups
Associated Lie algebras of p-groups of maximal class
lie-algebras
p-groups
A group acting on a $p$-group
group-theory
group-actions
p-groups
Any irreducible representation of a $p$-group over a field of characteristic $p$ is trivial.
abstract-algebra
representation-theory
p-groups
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
abstract-algebra
group-theory
p-groups
Question about a proof of: If $P$ is a finite $p$-group and $\langle 1\rangle\neq N\trianglelefteq P$, then $N\cap Z(P)\neq\langle 1\rangle$.
abstract-algebra
group-theory
proof-explanation
group-actions
p-groups
Power of commutator formula
abstract-algebra
group-theory
free-groups
p-groups
Let $G$ be a p-group. Let $H$ be a proper subgroup of $G$. Show that there exists $g$ $\in$ $G \setminus H$ such that $gHg^{-1}=H$.
group-theory
p-groups
The centre of a minimal nonabelian $p$-subgroup [closed]
group-theory
finite-groups
p-groups
The equivalence classes of $N\sim M\Leftrightarrow G/N\cong G/M$.
abstract-algebra
group-theory
finite-groups
p-groups
computational-algebra
What are central automorphisms used for?
group-theory
finite-groups
definition
intuition
p-groups
Is a product of $p$-subgroups still a $p$-subgroup?
group-theory
p-groups
Conjugacy classes of a $p$-group
group-theory
finite-groups
p-groups
Prove that there exists a $z \in Z(G)$ such that $yx = zxy$.
group-theory
finite-groups
normal-subgroups
p-groups
infinite abelian group where all elements have order 1, 2, or 4
group-theory
abelian-groups
p-groups
There exist infinite solvable $p$-groups with trivial centre. (Use a hint.)
group-theory
p-groups
infinite-groups
solvable-groups
wreath-product
Does every group whose order is a power of a prime p contain an element of order p?
group-theory
finite-groups
p-groups
Classify groups of order 27
abstract-algebra
group-theory
finite-groups
p-groups
groups-enumeration
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