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 L + n (resp. L n ) is isomorphic to a subgroup of the symmetric group S n (resp. the semi-direct product ( Z / 2 Z ) n ⋉ S n ).