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Statements

Subject Item

dbr:Group_isomorphism_problem

rdf:type

dbo:Disease

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Group isomorphism problem

rdfs:comment

In abstract algebra, the group isomorphism problem is the decision problem of determining whether two given finite group presentations present isomorphic groups. The isomorphism problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the word problem and the conjugacy problem. All three problems are undecidable: there does not exist a computer algorithm that correctly solves every instance of the isomorphism problem, or of the other two problems, regardless of how much time is allowed for the algorithm to run. In fact the problem of deciding whether a group is trivial is undecidable, a consequence of the Adian–Rabin theorem due to Sergei Adian and Michael O. Rabin.

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dbc:Group_theory dbc:Undecidable_problems

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n5:Group_isomorphism_problem?oldid=1058075546&ns=0

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1058075546

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dbr:Presentation_of_a_group dbr:Mathematische_Annalen dbr:Word_problem_for_groups dbr:Dover_Publications dbc:Group_theory dbr:Decision_problem dbr:Decidability_(logic) dbr:Michael_O._Rabin dbr:Cambridge_University_Press dbr:Sergei_Adian dbr:Max_Dehn dbr:Abstract_algebra dbr:Conjugacy_problem dbr:Group_(mathematics) dbr:Isomorphism dbc:Undecidable_problems dbr:Adian–Rabin_theorem

dbo:abstract

In abstract algebra, the group isomorphism problem is the decision problem of determining whether two given finite group presentations present isomorphic groups. The isomorphism problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the word problem and the conjugacy problem. All three problems are undecidable: there does not exist a computer algorithm that correctly solves every instance of the isomorphism problem, or of the other two problems, regardless of how much time is allowed for the algorithm to run. In fact the problem of deciding whether a group is trivial is undecidable, a consequence of the Adian–Rabin theorem due to Sergei Adian and Michael O. Rabin.

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n5:Group_isomorphism_problem