Аннотация:Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of the groups with an element of infinite order. We produce joining-stable invariants considering zero P-entropy systems and prove an analog of Pinsker's theorem establishing the disjointness of such systems with the actions of comletely positive P-entropy. Then we apply Poisson suspensions to get a class of the corresponding examples.