= Higman's embedding theorem
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= Higman embedding theorem
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A <finitely generated group> embeds in a <finitely presented group> if and only if it has a <recursive presentation of a group>. The necessity follows by enumerating proofs that substituted generator words are trivial in the larger <finite group presentation>. The sufficiency is the embedding theorem; it also applies to effectively countably generated recursive presentations after an effective two-generator embedding. This is the theorem of https://doi.org/10.1098/rspa.1961.0132[Subgroups of finitely presented groups].
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