On subgroups of free Burnside groups of large odd exponent

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We prove that every noncyclic subgroup of a free m-generator Burnside group B(m,n) of odd exponent n ≫ 1 contains a subgroup H isomorphic to a free Burnside group B(∞,n) of exponent n and countably infinite rank such that for every normal subgroup K of H the normal closure <K >ᵇ⁽ᵐ,ⁿ⁾ of K in B(m,n) meets H in K. This implies that every noncyclic subgroup of B(m,n) is SQ-universal in the class of groups of exponent n.