Newbetuts
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New posts in abelian-groups
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
group-theory
finite-groups
abelian-groups
least-common-multiple
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian [closed]
group-theory
abelian-groups
Automorphisms of infinite abelian groups
group-theory
abelian-groups
infinite-groups
Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?
abstract-algebra
group-theory
abelian-groups
direct-sum
Group of order $1225$ is abelian
abstract-algebra
group-theory
abelian-groups
normal-subgroups
sylow-theory
Is $\Bbb Q/\Bbb Z$ artinian as a $\Bbb Z$-module?
commutative-algebra
proof-verification
modules
abelian-groups
Quotient group $\mathbb Z^n/\ \text{im}(A)$ [duplicate]
abstract-algebra
matrices
group-theory
abelian-groups
In an abelian group, the elements of finite order form a subgroup.
abstract-algebra
group-theory
abelian-groups
Arnold's proof of Abel's theorem
complex-analysis
abelian-groups
proof-explanation
number of subgroups index $p$ equals number of subgroups order $p$
abstract-algebra
group-theory
finite-groups
abelian-groups
Group $\mathbb Q^*$ as direct product/sum
abstract-algebra
group-theory
proof-verification
abelian-groups
rational-numbers
When is the automorphism group $\text{Aut }G$ cyclic?
group-theory
finite-groups
abelian-groups
cyclic-groups
Coproducts in $\text{Ab}$
abstract-algebra
group-theory
category-theory
abelian-groups
Proof that a group is abelian if every square is the identity.
group-theory
proof-verification
abelian-groups
Help to show that $\bigoplus_{i\in\mathbb{N}}\mathbb{Z}\cong\operatorname{Hom}(\prod_{i\in\mathbb{N}}\mathbb{Z},\mathbb{Z})$.
abstract-algebra
group-theory
ring-theory
modules
abelian-groups
Let $G = \langle x, y \mid x^{7} = y^{3} = e,\; yxy^{−1} = x\rangle$. What is $|G|\,$?
abstract-algebra
group-theory
abelian-groups
group-presentation
combinatorial-group-theory
Problem on abelian group
group-theory
abelian-groups
abstract-algebra
Applications of the fact that a group is never the union of two of its proper subgroups
group-theory
abelian-groups
symmetric-groups
$\Bbb{Q}$ is not a finitely generated $\Bbb{Z}$-module
abstract-algebra
proof-verification
modules
abelian-groups
What is wrong with the following argument about splitting an exact sequence of abelian groups?
algebraic-topology
abelian-groups
exact-sequence
abelian-categories
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