  In this article we give a sufficient and necessary condition to determine
wether or not an element of the free group induces a non-trivial element of the
free Burnside group of sufficiently large odd exponent. This criterion can be
stated without any knowledge about Burnside groups, in particular about the
proof of its infiniteness. Therefore it provides a useful tool that we will use
later to study outer automorphisms of Burnside groups. We also state an
analogue result for periodic quotients of torsion-free hyperbolic groups.
