  Let $m, m', r, r',t, t'$ be positive integers with $r, r' \ge 2$. Let $L_r$
denote the ring that is universal with an invertible $1 \times r$ matrix. Let
$M_m(L_r^{\otimes t})$ denote the ring of $m \times m$ matrices over the tensor
product of $t$ copies of $L_r$. In a natural way, $M_m(L_r^{\otimes t})$ is a
partially ordered ring with involution. Let $PU_m(L_r^{\otimes t})$ denote the
group of positive unitary elements. We show that $PU_m(L_r^{\otimes t})$ is
isomorphic to the Brin-Higman-Thompson group $t V_{r,m}$; the case $t =1$ was
found by Pardo, that is, $PU_m(L_r)$ is isomorphic to the Higman-Thompson group
$V_{r,m}$. We survey arguments of Abrams, \'Anh, Bleak, Brin, Higman, Lanoue,
Pardo, and Thompson that prove that $t' V_{r',m'} \cong tV_{r,m} $ if and only
if $r' = r$, $t'=t$ and $ \gcd(m',r'-1) = \gcd(m,r-1)$ (if and only if
$M_{m'}(L_{r'}^{\otimes t'})$ and $M_m(L_r^{\otimes t})$ are isomorphic as
partially ordered rings with involution).
