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- Higmans_embedding_theorem abstract "In group theory, Higman's embedding theorem states that every finitely generated recursively presented group R can be embedded as a subgroup of some finitely presented group G. This is a result of Graham Higman from the 1960s.On the other hand, it is an easy theorem that every finitely generated subgroup of a finitely presented group is recursively presented, so the recursively presented finitely generated groups are (up to isomorphism) exactly the subgroups of finitely presented groups.Since every countable group is a subgroup of a finitely generated group, the theorem can be restated for those groups.As a corollary, there is a universal finitely presented group that contains all finitely presented groups as subgroups (up to isomorphism); in fact, its finitely generated subgroups are exactly the finitely generated recursively presented groups (again, up to isomorphism).Higman's embedding theorem also implies the Novikov-Boone theorem (originally proved in the 1950s by other methods) about the existence of a finitely presented group with algorithmically undecidable word problem. Indeed, it is fairly easy to construct a finitely generated recursively presented group with undecidable word problem. Then any finitely presented group that contains this group as a subgroup will have undecidable word problem as well.The usual proof of the theorem uses a sequence of HNN extensions starting with R and ending with a group G which can be shown to have a finite presentation.".
- Higmans_embedding_theorem wikiPageID "4061200".
- Higmans_embedding_theorem wikiPageLength "2127".
- Higmans_embedding_theorem wikiPageOutDegree "14".
- Higmans_embedding_theorem wikiPageRevisionID "634854968".
- Higmans_embedding_theorem wikiPageWikiLink Category:Infinite_group_theory.
- Higmans_embedding_theorem wikiPageWikiLink Category:Theorems_in_group_theory.
- Higmans_embedding_theorem wikiPageWikiLink Corollary.
- Higmans_embedding_theorem wikiPageWikiLink Countable.
- Higmans_embedding_theorem wikiPageWikiLink Countable_set.
- Higmans_embedding_theorem wikiPageWikiLink Finitely_generated_group.
- Higmans_embedding_theorem wikiPageWikiLink Finitely_presented_group.
- Higmans_embedding_theorem wikiPageWikiLink Generating_set_of_a_group.
- Higmans_embedding_theorem wikiPageWikiLink Graham_Higman.
- Higmans_embedding_theorem wikiPageWikiLink Group_theory.
- Higmans_embedding_theorem wikiPageWikiLink HNN_extension.
- Higmans_embedding_theorem wikiPageWikiLink Presentation_of_a_group.
- Higmans_embedding_theorem wikiPageWikiLink Recursively_presented_group.
- Higmans_embedding_theorem wikiPageWikiLink Subgroup.
- Higmans_embedding_theorem wikiPageWikiLink Word_problem_for_groups.
- Higmans_embedding_theorem wikiPageWikiLinkText "Higman embedding theorem".
- Higmans_embedding_theorem wikiPageWikiLinkText "Higman's embedding theorem".
- Higmans_embedding_theorem hasPhotoCollection Higmans_embedding_theorem.
- Higmans_embedding_theorem wikiPageUsesTemplate Template:Reflist.
- Higmans_embedding_theorem subject Category:Infinite_group_theory.
- Higmans_embedding_theorem subject Category:Theorems_in_group_theory.
- Higmans_embedding_theorem comment "In group theory, Higman's embedding theorem states that every finitely generated recursively presented group R can be embedded as a subgroup of some finitely presented group G.".
- Higmans_embedding_theorem label "Higman's embedding theorem".
- Higmans_embedding_theorem sameAs m.0bg3cm.
- Higmans_embedding_theorem sameAs Q17029787.
- Higmans_embedding_theorem sameAs Q17029787.
- Higmans_embedding_theorem wasDerivedFrom Higmans_embedding_theoremoldid=634854968.
- Higmans_embedding_theorem isPrimaryTopicOf Higmans_embedding_theorem.