Property Pnaive for acylindrically hyperbolic groups

We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the P-naive property: for any finite collection of elements h(1),...,h(k), there exists another element gamma not equal 1 such that for all i, < h(i), gamma > = < hi > * <gamma >. We also show that if a collection of subgroups H-1,...,H-k is a hyperbolically embedded collection, then there is gamma not equal 1 such that for all i, < H-i, gamma > = < Hi >*<gamma >.