The object for Dawn dish liquid is that it cuts the oils on the fleas and they drown. I don't think it actually kills the fleas unless they are in the bath. I have used it for our animals. Been through at least 50+ cats in the last 30 years. Raising and finding homes for most of them. Now we are into the Frontline and down to 10 cats and one small dog. Sams and Walmart sell a Frontline look a like, not made by Frontline, Pet Armor. We have just started trying that on our cats. Might I also suggest flea combs, they work wonders. All that crap they comb out of your animals is flea larvae and blood left for them to dine on upon hatching. Gross, hey? Vacumning and sweeping. All flat surfaces where animals lay or walk. When you comb your animal, be quick and squish the fleas you find and clean comb off with kleenix so when you are done you can throw away all the larvae(little salt like looking things) right into the trash, preferable bag up in a zip lock. It is full scale war to get rid of them. Have to attack on all fronts.
Wash bedding in hot water if possible(not hand made quilts) and hang outside. Animal beds need vacumning constantly and carpets, evey floors, vacumn, vacumn, vacumn and then take vac out and clean it outside dumping it right in trash. Don't forget all floors, basement too need vacumning. Nope, not easy keeping our fur babies comfy, but it is worth it.