Embeddings into simple free products

Meier, David

doi:10.1090/S0002-9939-1985-0773986-5

Embeddings into simple free products
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Proc. Amer. Math. Soc. 93 (1985), 387-392 Request permission

Abstract:

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 $S$.

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