In mathematics, a sofic group is a group whose Cayley graph is an initially subamenable graph, or equivalently a subgroup of an ultraproduct of finite-rank symmetric groups such that every two elements of the group have distance 1.[1] They were introduced by Gromov (1999) as a common generalization of amenable and residually finite groups. The name "sofic", from the Hebrew word סופי meaning "finite", was later applied by Weiss (2000), following Weiss's earlier use of the same word to indicate a generalization of finiteness in sofic subshifts.
The class of sofic groups is closed under the operations of taking subgroups, extensions by amenable groups, and free products. A finitely generated group is sofic if it is the limit of a sequence of sofic groups. The limit of a sequence of amenable groups (that is, an initially subamenable group) is necessarily sofic, but there exist sofic groups that are not initially subamenable groups.[2]
As Gromov proved, Sofic groups are surjunctive.[1] That is, they obey a form of the Garden of Eden theorem for cellular automata defined over the group (dynamical systems whose states are mappings from the group to a finite set and whose state transitions are translation-invariant and continuous) stating that every injective automaton is surjective and therefore also reversible.[3]
^ abCeccherini-Silberstein & Coornaert (2010) p. 276
Is every discrete, countable groupsofic? (more unsolved problems in mathematics) In mathematics, a soficgroup is a group whose Cayley graph is an initially...
"finite". It may refer to: Sofic subshift, a shift space whose forbidden words form a regular language Soficgroup, a group whose Cayley graph is an initially...
surjunctive groups include all locally residually finite groups, all free groups, all subgroups of surjunctive groups, all abelian groups, all soficgroups, and...
most widely studied shift spaces are the subshifts of finite type and the sofic shifts. In the classical framework a shift space is any subset Λ {\displaystyle...
theory of amenable groups (with Don Ornstein), mean dimension (with Elon Lindenstrauss), introduction of sofic subshifts and soficgroups. The road coloring...
Industry Association's annual Special Operations Forces Industry Conference (SOFIC), in May 2019, FN unveiled a prototype of its Mk 48 Mod 2 machine gun chambered...
information theory; University of Oslo, January 7–11, 2019 Workshop on Sofic and Hyperlinear Groups and the Connes Embedding Conjecture; UFSC Florianopolis, Brazil;...
Conference (SOFIC) in Tampa, Fla. And Logos Technologies has been working on a version weighing nearly 20 pounds for smaller UAVs, or Group 2 unmanned...
original on 2015-04-05. Retrieved 2011-09-30. Prior RL, Cao G, Martin A, Sofic E, McEwen J, O'Brien C, et al. (1998). "Antioxidant Capacity As Influenced...
every finitely presented periodic group finite? Is every group surjunctive? Is every discrete, countable groupsofic? Problems in loop theory and quasigroup...
dynamics. Important special cases include subshifts of finite type and sofic systems. The term ergodic is commonly thought to derive from the Greek words...
terms of symbolic dynamics, this means that the pinwheel tilings form a sofic subshift. Radin and Conway proposed a three-dimensional analogue which was...
June 2022. Cervantes, Marcos (2020). "Delivering Dominance" (PDF). NDIA. SOFIC 2020. Archived from the original (PDF) on 13 November 2020. Retrieved 6...
181-223. Th. Fernique and N. Ollinger, Combinatorial substitutions and sofic tilings, Journees Automates Cellulaires 2010, J. Kari ed., TUCS Lecture...
of closed manifolds, the Prouhet–Thue–Morse system, the Chacon system, sofic systems, context-free systems and block-coding systems. Research has reported...
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