= Word problem for a group
{wiki=Word_problem_for_groups}
= Word problem for groups
{synonym}
For a fixed finitely generated <group> with specified generators, its word problem asks for an algorithm deciding whether an input word represents the identity. For a finitely presented group, positive answers can be enumerated from the relators, but there need not be an algorithm deciding both positive and negative answers. An effective reduction from a nonrecursive <halting set> proves unsolvability.
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