The group word problem for a finitely generated group asks whether a given finite word in its group generators and their inverses represents the identity element (Milne 2025, p. 37). It is decidable if one algorithm terminates on every word and answers this question correctly. This decision property is independent of the chosen finite set of group generators.
Group Word Problem
See also
Classifying Space, Finitely Generated, Finitely Presented Group, Group, Group Generators, Group Presentation, Recursively Undecidable, Simple Group, Word, Word ProblemExplore with Wolfram|Alpha
References
Milne, J. S. Group Theory, ver. 4.01. 2025. https://www.jmilne.org/math/CourseNotes/GT.pdf.Cite this as:
Weisstein, Eric W. "Group Word Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupWordProblem.html