Is it permissible for a woman to work and travel on a mission abroad, such as to America?

A woman is not permitted to travel without a mahram (definition). The prohibition of this has been reported in various forms in authentic hadiths, and there is a consensus on its impermissibility except in cases of dire necessity. If a woman's work requires her to travel frequently without a mahram, then it becomes impermissible, because it can lead to fitna (strife/temptation) and corruption. It is also difficult for a mahram to accompany her on every trip, and whatever leads to the forbidden is itself forbidden.