List questions from free-groups | MathQA

Question about groups where generators are interchangable

Published on 08 Dec 2022 - 19:13

Show that there is a unique ring homomorphism from $\mathbb{Z}$ into any ring.

Published on 09 Dec 2022 - 16:39

Free Product on 3 Groups confusion

Published on 15 Dec 2022 - 3:11

Step in a proof that $G:=\langle x,y \mid x^n,y^2, (xy)^2\rangle$ is isomorphic to the dihedral group $D_n$

Published on 29 Mar 2026 - 18:10

$\langle a,b\mid ab=1\rangle\cong \mathbb{Z}$

Published on 30 Dec 2022 - 17:59

In the group $G=\langle r,s,t\mid r^2=s^3=t^3=rst\rangle,$ the element $rst$ has order $2$

Published on 28 Mar 2026 - 3:33

is $F_2$ a subgroup of any other $F_n$ for $n\geq 2$

Published on 09 Jan 2023 - 23:25

Question on the standard algebraic topology proof that a subgroup of a free group is free

Published on 11 Jan 2023 - 18:19

What is the induced homomorphism of the covering map $p : Y \to X : z \mapsto z^3 - 3z$ on the fundamental groups?

Published on 18 Jan 2023 - 8:06

If $F$ is free and $R$ is normal in $F$, then $F/R'$ is torsion-free, where $R'=[R,R]$

Published on 23 Feb 2026 - 9:34