By adapting the classical proof of Jordan's theorem on finite subgroups of linear groups, we show that every approximate subgroup of the unitary group U_n(C) is almost abelian.
BREUILLARD, EMMANUEL and GREEN, BEN
"Approximate groups III: the unitary case,"
Turkish Journal of Mathematics: Vol. 36:
2, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss2/2