  In this paper we study the effects of hybridization in the superconducting
properties of a two-band system. We consider the cases that these bands are
formed by electronic orbitals with angular momentum, such that, the
hybridization $V(\mathbf{k})$ among them can be symmetric or antisymmetric
under inversion symmetry. We take into account only intra-band attractive
interactions in the two bands and investigate the appearance of an induced
inter-band pairing gap. We show that (inter-band) superconducting orderings are
induced in the total absence of attractive interaction between the two bands,
which turns out to be completely dependent on the hybridization between them.
For the case of antisymmetric hybridization we show that the induced inter-band
superconductivity has a p-wave symmetry.
