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New posts in abelian-groups
For finite abelian groups, show that $G \times G \cong H \times H$ implies $G \cong H$
abstract-algebra
group-theory
finite-groups
abelian-groups
Let $H\leq G$. Prove $x^{-1}y^{-1}xy\in H\text{ }\forall x,y\in G \iff H\trianglelefteq G \text{ and } G/H \text{ is abelian}$.
abstract-algebra
group-theory
abelian-groups
normal-subgroups
quotient-group
The existence of a group automorphism with some properties implies commutativity.
abstract-algebra
group-theory
finite-groups
abelian-groups
Non-Abelian groups and subgroups
abstract-algebra
group-theory
abelian-groups
(finitely generated finite by abelian) implies (abelian by finite)
group-theory
finite-groups
abelian-groups
group-extensions
Group theory exercise from Judson text
abstract-algebra
group-theory
abelian-groups
Manipulating quotients and direct sums of abelian groups
abstract-algebra
group-theory
abelian-groups
If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$
group-theory
abelian-groups
normal-subgroups
Prove that that $U(n)$ is an abelian group.
group-theory
abelian-groups
On the Factor group $\Bbb Q/\Bbb Z$ [duplicate]
abstract-algebra
group-theory
abelian-groups
cyclic-groups
Let $G$ be a finite Abelian group that has exactly one subgroup for each divisor of $|G|$. How does this imply that $G$ is cyclic? [duplicate]
group-theory
finite-groups
abelian-groups
cyclic-groups
What is the abelianization of $\langle x,y,z\mid x^2=y^2z^2\rangle?$
abstract-algebra
group-theory
abelian-groups
combinatorial-group-theory
${\rm Aut}(G)$ is cyclic $\implies G$ is abelian
group-theory
solution-verification
abelian-groups
group-isomorphism
automorphism-group
Is $\mathbb{Z}^2$ cyclic?
abstract-algebra
group-theory
abelian-groups
cyclic-groups
Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian?
abstract-algebra
group-theory
abelian-groups
Size of a linear image of a cube in $\mathbb{Z}^d$
linear-algebra
group-theory
modules
abelian-groups
For abelian groups: does knowing $\text{Hom}(X,Z)$ for all $Z$ suffice to determine $X$?
abstract-algebra
group-theory
modules
abelian-groups
If $A$ is an additive abelian group and $\alpha, \beta \in{\rm End}(A)$, show $\alpha+\beta\in{\rm End}(A)$
abstract-algebra
group-theory
abelian-groups
group-homomorphism
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
abstract-algebra
group-theory
abelian-groups
Every group with 5 elements is an abelian group
group-theory
finite-groups
abelian-groups
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