New posts in abelian-groups

Prove: A group $G$ is abelian if and only if the map $G\rightarrow G$ given by $x\mapsto x^{-1}$ is an automorphism.

Squeeze Theorem for Abelian Groups

Classify finitely generated modules over the ring $\mathbb{C}[\epsilon]$ where $\epsilon^2=0$

Distributions over locally compact Abelian groups: when can they be Fourier transformed?

Prove the order of each nonindentity element of $G$ is $p$. [closed]

An abelian group of order 100

Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$

A problem about abelian group

Group tables for a group of four elements.

If N and every subgroup of N is normal in G then G/N is abelian .

Equality of rank for homology and cohomology groups via the universal coefficient theorem

Is the group of positive rationals under multiplication isomorphic to its subgroup consisting of rationals with odd numerators and denominators?

"Classify $\mathbb{Z}_5 \times \mathbb{Z}_4 \times \mathbb{Z}_8 / \langle(1,1,1)\rangle$"

If $H$ is a subgroup of a finite abelian group $G$, then $G$ has a subgroup that is isomorphic to $G/H$.

Show that any subgroup of a finitely generated abelian group is finitely generated?

Does the splitting lemma hold without the axiom of choice?

Are there any non-obvious colimits of finite abelian groups?

Prove that every proper subgroup of the group of all $2^n$-th roots of unity is finite.

Prove $G$ is abelian if $f(f(x)) = x$?