Specification and partial hyperbolicity for flows

We prove that if a flow exhibits a partially hyperbolic attractor Λ with splitting and two periodic saddles with different indices such that the stable index of one of them coincides with the dimension of Es then it does not satisfy the specification property. In particular, every sectional-hyperbolic attractor with the specification property is hyperbolic. As an application, we prove that no geometric Lorenz attractor satisfies the specification property.