Yes, as Sue said both gregii and battalinii are the species names. I do my searches by genus and cultivar, as if you do it for something with a common name like Lilac as the cultivar, you're going to get a lot of hits from all over the plant kingdom.
For Tulipa battalinii Bronze Charm for ex.
Tulipa is the genus
Tulip the common
battalinii the species
Bronze Charm is the cultivar
I think species is the only correct way to say it, not specie.
