I just came across Unsolved Problems in Group Theory, of which there are 100's of very specific, detailed problems, such as these:
15.68. Does there exist an infinite finitely generated 2-group (of finite exponent) all of whose proper subgroups are locally finite?
16.78. Do there exist linear non-abelian simple groups without involutions?
17.9. Is there a group containing a left Engel element whose inverse is not a left Engel element?
In learning about the basics of group theory, it is an interesting subject. It has applications in many fields. But the applications as far as I can tell rely on the common body of knowledge in group theory (or in a mathematical field). Basically stuff you can find in textbooks or Wikipedia.
So I was wondering if one could explain the value in answering these 100's of questions. I can see answering some questions like a very relevant theorem perhaps, but the detail of these questions is very deep and there are so many. It seems like many more questions could be proposed as well, lots of edge-cases etc.. I know I am missing a lot of context so I hope this comes across okay. I am hoping to find it interesting, right now it feels overwhelming :)