  In this note we shall prove that the Stone-\v{C}ech compactification of
$\mathcal{L}^n$ is the space $\bar{\mathcal{L}}^n$ where $\bar{\mathcal{L}}$ is
the extended long line, namely, $\mathcal{L}$ together with its ends $\pm
\Omega$. We give a similar description for the Stone-\v{C}ech compactification
of the cartesian power of the semi-closed half-long line $\mathcal{L}_+$. As an
application we show that any torsion subgroup of the group of all
homeomorphisms of $\cj^n$ (resp. $\cl^n$) is isomorphic to a subgroup of the
symmetric group $S_n$ (resp. the semidirect product $(\bz/2\bz)^n\ltimes S_n$).
