Torsion subgroups of the homeomorphism groups of products of long line

Denote by L (resp. L+) the long line (resp. half-long line). In this note we show that, for n⩾1, any torsion subgroup of the group of all homeomorphisms of (resp. Ln) is isomorphic to a subgroup of the symmetric group Sn (resp. the semi-direct product n(Z/2Z)⋉Sn).