ON THE FINITENESS PROPERTIES OF GROUPS

By Z. Tabatabaei, M. Naghshinehfard. 2013

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Finite Factor Representations of Higman-Thompson groups (2012, background): “Note that the commutator subgroups of groups in fFn;rg or fGn;rg are simple [2], [8].”
Topological full groups of one-sided shifts of finite type (2012, background): “It is known that Vn,r is finitely presented, the commutator subgroup D(Vn,r) is simple, and the abelianization Vn,r/D(Vn,r) is trivial when n is even and is Z2 when n is odd ([4]).”
On subgroups of R. Thompson's group $F$ (2015, unknown): “Brown [4]: it is a version of F where all slopes of the piecewise-linear functions are powers of 3 and break points of the derivative are finite 3-adic fractions.”
Simple locally compact groups acting on trees and their germs of automorphisms (2010, methodology): “6.3. Abstract commensurators and Higman{Thompson groups We shall need to consider the so-called Higman{Thompson groups, an excellent introduction to which can be consulted in [ Bro87 ,x4].”
Combinatorial algebra : syntax and semantics (2014, unknown): “That was the first example of a finitely presented infinite simple group (for more on this see [54] and [62]).”
On Jones' subgroup of R. Thompson group $F$ (2015, background): “Equivalently, the group F can be defined using dyadic subdivisions [1].”
Etale groupoids arising from products of shifts of finite type (2015, background): “Brown [8] proved that Vk,r is of type F∞.”