Any kind of dish soap can kill fleas. It works whether it is used as a flea trap or used directly in a dog or cat's bath.
A flea trap can be made with dish soap by pouring one part soap and three parts water into a shallow dish. Place the dish near areas where the pet is commonly found. Mix the soap and water together, then place a small directional lamp directly over the dish so that the light is pointed right at the soapy mixture. At night, turn off all other surrounding lights so that the fleas gravitate toward the only heat source: the lamp. The soapy water keeps the fleas from jumping out of the dish and drowns them.
Cats and dogs can also be bathed in a dish-soap bath to directly kill the fleas. The soap destroys a flea's exoskeleton. Use a comb to remove leftover dead fleas.