Searching for is not an admission of weakness. It is an admission that you are taking the subject seriously. Abstract algebra is a foreign language of logic, and everyone needs a translator sometimes.
The best "solution manual" is not a PDF. It is a process: a book of abstract algebra pinter solutions
Most abstract algebra textbooks (like Dummit & Foote or Artin) are encyclopedic. They are written for reference , not for reading . Pinter, by contrast, wrote his book to be read like a novel. Searching for is not an admission of weakness
Since [G:H] = 2, there are exactly two left cosets: H and gH for g ∉ H. The same for right cosets. For any g ∉ H, gH = G \ H = Hg, so gH = Hg. For g ∈ H, trivial. Hence H is normal. The best "solution manual" is not a PDF
There is a semi-secret Facebook group called "Dover Math & Science Readers." In it, dozens of self-learners post their Pinter solutions weekly. Because Dover reprints classic texts, the community is passionate and non-judgmental. Search the group’s history for "Pinter Chapter X" before you post your own problem.