On the tightness of left‐invariant contact structures

Abstract We prove that all left‐invariant contact structures on three‐dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left‐invariant contact structure, other than . We then make use of such factorization property to construct embeddings of left‐invariant contact structures into the standard contact structure on .