New posts in finitely-generated

Does ZFC decide every question about finitely generated groups?

Why any countable subset of $\mathbb{R}→\mathbb{R}$ is generated by a finite set under composition?

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

For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$? [duplicate]

Versions of Nakayma's Lemma

Is the cyclic group $\langle x\rangle$ always a subgroup of $G$ for any $x\in G$?

subgroups of finitely generated groups with a finite index

Must $k$-subalgebra of $k[x]$ be finitely generated?

Can I recover a group by its homomorphisms?

Finitely generated module with a submodule that is not finitely generated [duplicate]

Simple question about finitely generated algebras

Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$