The Short Version:
How do you study Galois theory at a university where no-one else studies Galois theory?
You apply to attend a different university and switch schools after you complete your bachelor's degree
The Long Version
Use Google to find living experts in Galois theory.
Get these people's email address. Talk to them.
The best ...
I didnt know there are universities that do not offer a module on algebra which includes Galois theory, this seems a bit troubling.
Generally: don't do it. Pick only a topic which is known at your university or switch to a different univerisity. Your argument that new research groups are founded is not valid, since this either happens by hiring somebody from ...
This is harder to do for most undergraduate students since they don't have sufficient experience to get by without feedback on what they study. Normally learning requires both reinforcement and feedback. Reinforcement comes from applying what you study in some way, exercises for example. Feedback normally comes from a professor evaluating what you produce. ...