Muslims can wear deodorant even if it contains alcohol. Depending on the way the individual Muslim interprets the Quran, he may choose not to wear deodorant.
Muslim women are not allowed to wear perfume in public, but if a woman and her father or husband agree that deodorant is not considered perfume, she may wear it. Muslims are not permitted to drink alcohol, but a deodorant containing alcohol is allowed. Alcohol from deodorant is permitted because it is wiped on the body and is not ingested or discharged from the body. Before prayer, a Muslim may wash away deodorant if he or his imam believes that deodorant is dirty.