A sofic group is a countable group for which every finite portion of the multiplication table can be approximated arbitrarily accurately by permutations of a finite set. Products must agree on all but an arbitrarily small fraction of the set, while distinct group elements must act differently on almost every point. The notion was introduced by Gromov (1999), and the term was introduced by Weiss (2000).
Sofic Group
See also
Countable Set, Group, Multiplication Table, Permutation, Soficity ConjectureExplore with Wolfram|Alpha
References
Gromov, M. "Endomorphisms of Symbolic Algebraic Varieties." J. Eur. Math. Soc. 1, 109-197, 1999. https://doi.org/10.1007/PL00011162.Weiss, B. "Sofic Groups and Dynamical Systems." Sankhyā Ser. A 62, 350-359, 2000.Cite this as:
Weisstein, Eric W. "Sofic Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SoficGroup.html