On virtual chirality of 3‐manifolds

We prove that if a prime 3‐manifold is not finitely covered by the 3‐sphere or a product manifold, then is virtually chiral, that is, it has a finite cover that does not admit an orientation‐reversing self‐homeomorphism. In general, if a 3‐manifold contains a virtually chiral prime summand, then it is virtually chiral.