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Is there an example of a finitely presented infinite group in which every element has finite order? Or, is it known that every finitely presented infinite group has an element of infinite order? I as …

I've read that every finitely generated one relator group embeds in a two generator one relator group, and that this fact follows from the Freiheitssatz. Unfortunately, the only proof I can find of …

Suppose $G$ has the presentation $\langle t, x_1, x_2, ... | R \rangle$ where each relator in $R$ has the form $t^{-1}x_it = x_j$ for some $i,j$. Does $G$ have an element of order 2? This is an HNN e …

An interesting fact was relayed to me in another question of mine that If $M$ is any closed manifold with universal cover homeomorphic to $R^n$ for $n>1$ then $\pi_1(M)$ is freely indecomposable. …

A lot of work has been done on determining whether particular classes of groups are coHopfian, in particular the (sufficiently large) braid groups $B_n$ modulo center, and certain classes of 3-manifol …