It is shown that a minimal system is a d-step pro-nilsystem if its enveloping semigroup is a d-step top-nilpotent group, answering an open question by Donoso. Thus, combining the previous result of Donoso, it turns out that a minimal system is a d-step pro-nilsystem if and only if its enveloping semigroup is a d-step top-nilpotent group.

Meeting ID: 842 4054 6345 Passcode: 023053