Newbetuts

Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. How to prove that $G$ is an abelian group? [duplicate]

Is there a surjective morphism from an infinite direct product of copies of $\mathbb{Z}$ to an infinite direct sum of copies of $\mathbb{Z}$?

Non-trivial homomorphism between multiplicative group of rationals and integers

Direct sum and direct product of infinitely many abelian groups are not isomorphic

Does every ring with unity arise as an endomorphism ring?

Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.

Property of abelianization

Does an abelian subgroup inject into the abelianisation of the whole group? [closed]

If $G$ is abelian such that $mG=G$ for some $m\in\Bbb{Z}$ then every short exact sequence splits

Classify $\mathbb{Z} \times \mathbb{Z}/ \langle (3,1), (8,2) \rangle $ via fundamental theorem of finitely generated abelian groups

Let $G$ be an Abelian group with odd order. Show that $\varphi : G \to G$ such that $\varphi(x)=x^2$ is an automorphism

What is $\Bbb Z^n/(a_1, \dots, a_n)$ or $\Bbb Z^n / I$ isomorphic to?

Non-abelian group with infinitely many abelian subgroups

Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.

A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.

Can one distinguish finite groups by their maps from abelian groups?

Equivalences and isomorphisms of short exact sequences

New posts in abelian-groups

Let $G$ be a group, where $(ab)^3=a^3b^3$ and $(ab)^5=a^5b^5$. How to prove that $G$ is an abelian group? [duplicate]

Example of Intersection of Pure Subgroup which is not Pure

$G$ abelian if $\Leftrightarrow$ all its irreducible representations are of degree $1$

Subgroups of finite abelian groups.

Is there a surjective morphism from an infinite direct product of copies of $\mathbb{Z}$ to an infinite direct sum of copies of $\mathbb{Z}$?

Non-trivial homomorphism between multiplicative group of rationals and integers

Direct sum and direct product of infinitely many abelian groups are not isomorphic

Does every ring with unity arise as an endomorphism ring?

Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.

Property of abelianization

Does an abelian subgroup inject into the abelianisation of the whole group? [closed]

If $G$ is abelian such that $mG=G$ for some $m\in\Bbb{Z}$ then every short exact sequence splits

Classify $\mathbb{Z} \times \mathbb{Z}/ \langle (3,1), (8,2) \rangle $ via fundamental theorem of finitely generated abelian groups

Let $G$ be an Abelian group with odd order. Show that $\varphi : G \to G$ such that $\varphi(x)=x^2$ is an automorphism

What is $\Bbb Z^n/(a_1, \dots, a_n)$ or $\Bbb Z^n / I$ isomorphic to?

Non-abelian group with infinitely many abelian subgroups

Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.

A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.

Can one distinguish finite groups by their maps from abelian groups?

Equivalences and isomorphisms of short exact sequences