Questions tagged [one-relator-groups]

Is there a one-relator group with property (T)? That is, is there an $n > 2$, and some $x \in F_n$ (the free group on $n$ generators) such that the quotient of $F_n$ by the normal subgroup ...

I know that not every finitely-presented group may be embedded into a one-relator group, for example because of a theorem of Magnus stating that the word problem is solvable in one-relator groups. But ...

Every 1-related group $G$ with at least 2 generators is an HNN extension of another 1-related group $G_1$ with free associated subgroups. Indeed, if the total exponent of one letter in the relator is ...

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 ...

Roughly speaking, I want to know whether one-relator groups only have 'obvious' free splittings. Consider a one-relator group $G=F/\langle\langle r\rangle\rangle$, where $F$ is a free group. Is it ...