Newbetuts

What are the values of $a$ and $b$ so that $\Bbb Z_2\times\Bbb Z_3\times\Bbb Z_4\times\Bbb Z_9$ is isomorphic with $\Bbb Z_a\times\Bbb Z_b$?

Singular homology with coefficients in a ring versus in an abelian group

How many non-isomorphic abelian groups of order $\kappa$ are there for $\kappa$ infinite?

Prove/disprove: Let $G$ be abelian and $n\in\Bbb N$. Then $\{ g\in G:|g| \leq n\} $ forms a subgroup of $G$ [closed]

About direct sum of abelian groups and quotient

Is every group the unit group of some ring?

Characterization of the isomorphic semidirect products

Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$

Are these exactly the abelian groups?

Embedding torsion-free abelian groups into $\mathbb Q^n$?

Prove that $(a_1a_2\cdots a_n)^{2} = e$ in a finite Abelian group

A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?

Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.

What is the rank of a subgroup $H$ of finite index $e$ of a free abelian group $G$ of rank $n$?

Subgroups containing kernel of group morphism to an abelian group are normal. [closed]

For which $n$, $G$ is abelian?

Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$ [duplicate]

New posts in abelian-groups

$(G,\circ)$ is an abelian group, where $x\circ y=\frac{x+y+a(1+xy)}{1+xy+a(x+y)}$

How can we bound the number of subgroups of a finite abelian group?

Show that any abelian transitive subgroup of $S_n$ has order $n$

What are the values of $a$ and $b$ so that $\Bbb Z_2\times\Bbb Z_3\times\Bbb Z_4\times\Bbb Z_9$ is isomorphic with $\Bbb Z_a\times\Bbb Z_b$?

Singular homology with coefficients in a ring versus in an abelian group

How many non-isomorphic abelian groups of order $\kappa$ are there for $\kappa$ infinite?

Prove/disprove: Let $G$ be abelian and $n\in\Bbb N$. Then $\{ g\in G:|g| \leq n\} $ forms a subgroup of $G$ [closed]

About direct sum of abelian groups and quotient

Is every group the unit group of some ring?

Characterization of the isomorphic semidirect products

Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$

Are these exactly the abelian groups?

Embedding torsion-free abelian groups into $\mathbb Q^n$?

Prove that $(a_1a_2\cdots a_n)^{2} = e$ in a finite Abelian group

A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?

Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.

What is the rank of a subgroup $H$ of finite index $e$ of a free abelian group $G$ of rank $n$?

Subgroups containing kernel of group morphism to an abelian group are normal. [closed]

For which $n$, $G$ is abelian?

Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$ [duplicate]