Thompson's group 
is the group under composition of
increasing piecewise linear homeomorphisms
of ![[0,1]](/images/equations/ThompsonsGroupF/Inline2.svg)
having finitely many pieces, dyadic rational breakpoints,
and slopes that are integral powers of 2. A dyadic rational
has the form 
for integers 
and 
. The maps
fix both endpoints of the interval.
Thompson's group 
is distinct from the sporadic Thompson group.
Chaudkhari et al. (2026) proved that Thompson's group 
is a sofic group, as are the
related Thompson's group T and V.
The proof establishes soficity of V
and uses the inclusions 
. Chaudkhari
et al. (2026) credit ChatGPT with an earlier, weaker proof
for 
, while the presented argument for V
was developed by the authors.
