Embeddings into Simple Free Products
David L. Meier · Proceedings of the American Mathematical Society · 1985
We prove that a countable group $G$ can be embedded into a two-generator simple group $S$ which is an amalgamated free product of groups $G * {F_1}$ and $F$, where $F$ and ${F_1}$ are free groups on two generators. $S$ is also the product of two commuting free subgroups. If $G$ has solvable word problem, then we can construct a recursive presentation for $S$.