a group is said to be frobenius stable if every function from the group to unitaries that is "almost multiplicative" in the point-frobenius norm topology is "close" to a genuine representation of the group in the same topology. in this talk, i will summarize my proof that finitely generated nilpotent groups are frobenius stable if and only if they are virtually cyclic. i will also explain what the same techniques say about operator norm. this generalizes explicit counterexamples developed by voiculescu and kazhdan.