A countable discrete group is said to be Frobenius stable if every function from the unitary matrices that “almost multiplicative” in norm “close” a representation norm. The purpose of this paper show finitely generated nilpotent groups are not virtually cyclic stable. Our argument proves same result for other unnormalized Schatten p-norms with 1<p≤∞.

We prove an upper bound for the asymptotics of counting functions number fields with nilpotent Galois groups.