Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Agh yes of-course I should have added that both my divisors have positive degree (otherwise, as you say, it's very easy to get counterexamples) ... what would be a counterexample with a divisor of positive degree ?
@Derek Holt: thanks for the awesome reference ... could you slightly elaborate the point why the restriction map $H^2(G/A, A)\to H^2(P/A, A)$ is injective ? Is there any references for this ?
@Geoff Robinson: Thank you very much for your comment , and I'm okay to use Group Cohomology (as I have also given the tag ...) ... could you please detail out a proof or give any reference ? Thanks again