$\DeclareMathOperator\FSym{FSym}\DeclareMathOperator\Sym{Sym}$*Notation: for $X$ a set, $\Sym(X)$ the group of permutations of $X$, and let $\FSym(X)$ be the subgroup of finitely supported permutations of $X$ (it is generated by transpositions).*

Let $G$ be an infinite group. Let $P_G$ be the subgroup of $\Sym(G)$ generated by left translations and $\FSym(G)$. Equivalently, these are permutations of $G$ that coincide with a left translation outside a finite subset.

Thus $P_G$ is naturally a semidirect product $\FSym(G)\rtimes G$. One can prove various things about this group (e.g., if $G$ is finitely generated so is $P_G$, the group $P_G$ is never finitely presented, never Kazhdan, etc. 

The case $G=\mathbf{Z}$ of this construction is particularly well-known (as far as I know it essentially appears in a 1937 paper of B.H. Neumann) and well-documented.

I remember reading a paper about groups $P_G$ (at least 10 years ago), including these results (or so of them). Despite significant efforts to find the right keywords, I wasn't able to locate it. Does anybody identify this (or any paper referring to this construction in general, not just $G=\mathbf{Z}$)?