Questions tagged [word-problem]

Can anyone give me an example of a very simple word problem, where by "simple" I mean that it has very few generators and relations, that is nevertheless insoluble. To make the question easier, I am ...

Given some group $G$ that is generated by $a$ and $b$, each of which has infinite order, and some free subgroup $N$ generated by $a^k$ and $b^k$, is there any algorithm that tells me if some $x \in G$ ...