Does Islam permits a Muslim girl to go abroad/overseas and study in the absence of a maharem?
Certainly women/females are permitted to pursue their education and study. And this ruling is completely independent of gender and where you're going (Islamic or secular culture).
However this travel/stay should not come into conflict with other Islamic rules e.g. in case of married woman, traveling in spite of the husband asking not to or giving up on his Islamic rights (more or less like this).
There is another exception to this rule, which too is unisex, is that if one fears of being subject to at-ta'arrub ba'd al-hijra * then it's not permissible to go to such a place.
And the Prophet (saww) said to even travel to China (mostly meaning a distant place) if you have to seek education/knowledge. That saying is independent of gender.
Question: What is the meaning of at-ta'arrub ba'd al-hijra which is one of the major sins?
Answer: Some jurists have said that during our time, it applies to residing in countries that may cause the loss of faith. It means the migration of a person from a country -where it is possible for him to learn the obligatory religious teachings and laws, and where it is possible for him to fulfill his obligations and refrain from what is forbidden- to a country where this possibility does not exist fully or partially.