An automatic group is a finitely generated group having a regular language of normal forms for which right multiplication by each generator is recognized synchronously by a finite automaton. Equivalently, these normal forms satisfy a uniform fellow-traveler property in the Cayley graph. Automatic groups have solvable word problem and include finite groups, finitely generated Abelian groups, and word-hyperbolic groups.
Automatic Group
See also
Automata Theory, Cayley Graph, Finite Automaton, GroupExplore with Wolfram|Alpha
References
Epstein, D. B. A.; Cannon, J. W.; Holt, D. F.; Levy, S. V. F.; Paterson, M. S.; and Thurston, W. P. Word Processing in Groups. Boston, MA: Jones and Bartlett, 1992.Cite this as:
Weisstein, Eric W. "Automatic Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AutomaticGroup.html