While sinks in kitchen islands are still not very popular, stoves are quite often located on islands.
Cooks like having the stove on the kitchen island because it allows for increased working room. Also, centralized stoves make for a more social atmosphere, especially when bar chairs are added to the island.
A flat stove built into the island (or any other place) is called a cooktop. However, stove-oven combinations can also be built into kitchen islands.
Electrical or gas lines must be brought up from the floor, through the crawlspace (or through the concrete slab, depending on your home).