Wear natural fabric clothing, such as cotton or linens. Skin can not breath thru things such as rayon or polyester. Use an antiperspirant, not a deodorant (or use one that has both).
If it is really a problem. See your doctor. There are some prescription antiperspirants that your doctor can prescribe. Also, there is a procedure that can be done to rid some of the sweat glands in the underarm area--it is sort of similar to a laser type treatment.
Mitchum deodorant is effective. If that is not strong enough, your doctor can prescribe something. Spicy foods make you sweat more, as does stress.
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Please inform me on some ways to control underarm wetness.