All Countable Groups have Cubic Presentations
Matthew A. Marcus · Proceedings of the American Mathematical Society · 1985
Let $G$ be a group with presentation such that each generator occurs at most countably many times in the set of relations. Then for all $n \geqslant 3$, $G$ is $n$-ic. In particular, for all $n \geqslant 3$, countable groups have $n$-ic presentations.