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New posts in abelian-groups
Prove that any two nontrivial subgroups of $\mathbb{Q}$ have nontrivial intersection
abstract-algebra
group-theory
abelian-groups
rational-numbers
Finite abelian $p$-group with only one subgroup size $p$ is cyclic
group-theory
finite-groups
abelian-groups
On Groups of Order 315 with a unique sylow 3-subgroup .
abstract-algebra
group-theory
finite-groups
abelian-groups
sylow-theory
Finite abelian groups - direct sum of cyclic subgroup
group-theory
finite-groups
abelian-groups
Rank-nullity theorem for free $\mathbb Z$-modules
linear-algebra
modules
homological-algebra
abelian-groups
Why is every abelian group the direct limit of its finitely generated subgroups?
category-theory
abelian-groups
Is every subgroup of infinite Boolean group finite?
abstract-algebra
group-theory
abelian-groups
boolean-algebra
infinite-groups
Additive group of rationals has no minimal generating set
abstract-algebra
group-theory
number-theory
abelian-groups
rational-numbers
Simple proof of the structure theorems for finite abelian groups
group-theory
finite-groups
abelian-groups
Justify $\frac{\mathbb{Z}_a\times \mathbb{Z}_b}{\langle a/c\rangle \times \langle b/d\rangle}$ is isomorphic to $\mathbb{Z}_c\times \mathbb{Z}_d$.
group-theory
abelian-groups
group-isomorphism
quotient-group
Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module
abstract-algebra
modules
abelian-groups
Why is the abelian group of points on an elliptic curve over a finite field isomorphic to the product of at most two cyclic groups?
algebraic-geometry
abelian-groups
elliptic-curves
cyclic-groups
abelian-varieties
How "abelian" can a non-abelian group be?
group-theory
finite-groups
abelian-groups
Can the semidirect product of two groups be abelian group?
abstract-algebra
group-theory
finite-groups
abelian-groups
If the tensor power $M^{\otimes n} = 0$, is it possible that $M^{\otimes n-1}$ is nonzero?
abstract-algebra
modules
examples-counterexamples
abelian-groups
tensor-products
How can I visualise groups in Group Theory
group-theory
abelian-groups
binary-operations
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
abstract-algebra
group-theory
abelian-groups
proof-explanation
normal-subgroups
Find an abelian infinite group such that every proper subgroup is finite
group-theory
abelian-groups
infinite-groups
Give an example of a noncyclic Abelian group all of whose proper subgroups are cyclic.
abstract-algebra
abelian-groups
cyclic-groups
Proving that a subgroup of a finitely generated abelian group is finitely generated
abstract-algebra
group-theory
abelian-groups
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