Thompson's group 
is the group of orientation-preserving piecewise
linear homeomorphisms of the circle 
having finitely many dyadic breakpoints,
slopes that are integral powers of 2, and preserving the dyadic rational points.
A dyadic rational point is represented by 
, for integers 
and 
(Chaudkhari et al. 2026).
The subgroup fixing the point represented by 0 is Thompson's group F. Allowing discontinuous dyadic piecewise-linear bijections gives Thompson's
group V. Chaudkhari et al. (2026) proved that 
is a sofic group, by embedding
it in Thompson's group V.
