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. It is decidable if one algorithm terminates on every word and answers this question correctly. This decision property is independent of the chosen finite generating set.
Group Word Problem
See also
Classifying Space, Finitely Generated, Finitely Presented Group, Group Presentation, Simple Group, 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