New posts in abelian-groups

Finite abelian group contains an element with order equal to the lcm of the orders of its elements

If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian [closed]

Automorphisms of infinite abelian groups

Does $A\oplus \mathbb{Z}\cong B\oplus \mathbb{Z}$ imply $A\cong B$?

Group of order $1225$ is abelian

Is $\Bbb Q/\Bbb Z$ artinian as a $\Bbb Z$-module?

Quotient group $\mathbb Z^n/\ \text{im}(A)$ [duplicate]

In an abelian group, the elements of finite order form a subgroup.

Arnold's proof of Abel's theorem

number of subgroups index $p$ equals number of subgroups order $p$

Group $\mathbb Q^*$ as direct product/sum

When is the automorphism group $\text{Aut }G$ cyclic?

Coproducts in $\text{Ab}$

Proof that a group is abelian if every square is the identity.

Help to show that $\bigoplus_{i\in\mathbb{N}}\mathbb{Z}\cong\operatorname{Hom}(\prod_{i\in\mathbb{N}}\mathbb{Z},\mathbb{Z})$.

Let $G = \langle x, y \mid x^{7} = y^{3} = e,\; yxy^{−1} = x\rangle$. What is $|G|\,$?

Problem on abelian group

Applications of the fact that a group is never the union of two of its proper subgroups

$\Bbb{Q}$ is not a finitely generated $\Bbb{Z}$-module

What is wrong with the following argument about splitting an exact sequence of abelian groups?