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• W1834284857 abstract "It is known that a finitely generated simple group is a subgroup of a finitely presented group if and only if it has a recursively enumerable set of defining relations, and that it has a recursively enumerable set of defining relations if and only if it has a solvable word problem. This chapter presents the results that a finitely generated group has a solvable word problem if and only if there is an embedding of the group into a finitely generated simple group that is a subgroup of a finitely presented group. It was shown that if a finitely generated group has a word problem that is solvable with respect to one presentation on a finite set of generators, then the word problem is solvable with respect to every presentation on a finite set of generators. Thus, it can be said that the word problem for a finitely generated group is solvable or unsolvable without referring to a specific presentation. The chapter also discusses the countable groups assuming that all the presentations referred to are on finite or countably infinite set of generators." @default.
• W1834284857 created "2016-06-24" @default.
• W1834284857 creator A5048108916 @default.
• W1834284857 date "1980-01-01" @default.
• W1834284857 modified "2023-09-28" @default.
• W1834284857 title "Embeddings into Finitely Generated Simple Groups Which Preserve the Word Problem" @default.
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• W1834284857 doi "https://doi.org/10.1016/s0049-237x(08)71348-x" @default.
• W1834284857 hasPublicationYear "1980" @default.
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