The pups that are produced on flower stalks are called bulbils. They will not usually grow roots on the stalk but can be easily rooted by placing them on top of soil and watering infrequently until there is new growth. Just be careful to detach them from the stalk with the minimum damage, and provide protection from direct sun during the rooting process, at least until there is evidence of root activity.
Here is one I started that way over the winter. The rocks I laid in around it helped keep the bulbil seated during the rooting process.
