I do have a fair amount of visual/geometric understanding of groups, but when I start solving problems I always wind up relying on my algebraic intuition, i.e. experience with forms of symbolic expression that arise from theorems, definitions, and brute symbolic manipulation. I even came up with a "physical" (far from perfect) interpretation of the first isomorphism theorem. But when I get to solving problems, it's as if this intuition might as well gets thrown out the window because it's almost useless. It's really frustrating . Of course, I could not solve all the problems, but there are problems I could successfully solve and have no idea what I'm writing. Is this perfectly normal?