New posts in Group Presentation

Can the map sending a presentation to its group be considered as a functor?

Is it possible to prove that a group is the only group of its order given some properties?

Presentation for the product of two cyclic groups

One missing step in proving $\mathbb{Z}\times \mathbb{Z} \cong \langle a,b\,|\, [a,b]=1\rangle$

Find the group with presentation $\langle x, y: xy=yx, x^5=y^3\rangle$.

How to approach proofs similar to "Show a group, $G$, is infinite if $G = \langle r, s, t\mid rst = 1\rangle $"

Proving the order of quaternion group is 8

A question about dihedral group

Showing $b^2 \notin \langle a \rangle$ for $V_{8n}=\langle a,b:a^{2n}=e, b^4 = e, ba=a^{-1}b^{-1},b^{-1}a=a^{-1}b\rangle.$

Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).