In The Kite Runner, does Assef specifically take Sohrab because he knew Sohrab was Hassan's son?Was it stated as such, or implied?
I find no evidence in the text of The Kite Runner to show that Assef had any idea that Sohrab was related to Hassan. It seems that Assef would have told Amir during his lengthy talk before the fight if he had actually known. I believe it is pure coincidence that Assef chose Sohrab from the orphanage, and there is no evidence that he could have possibly known his name or his origins. Amir never mentions the possibility in his narrative; likewise, Sohrab never mentions this notion to Amir afterward. Although it would have certainly been fitting revenge for Assef--to molest and rape the son of the Hazara he hated so much--Assef apparently did not see the connection between the father and son and their prowess with the slingshots.
I thought about this myself when I was reading the book, I looked for hidden clues in case I was missing anything eluding to the fact the Assef know Sohab was Hassan's son.
When Amir was describing the way Sohab looked I figured Assef must have seen the resemblence too but during their lengthy conversation just before the fight Assef mentioned nothing about it. Assef's character is quite clear to see, we see throughout the book his hatred for hazaras, Amir and Hassan-if he had known Sohab was Hassan's son there was no way he would not have used that knowledge to torture Amir with, in my opinion. Hearing/knowing that would hurt more than any physical violence and would be sadistic-exactly Assefs style.
Assef was humiliated by Hassan, and was injured by him as well. Having Hassan killed was not enough for Assef, as Assef seems to have a rather vindictive, violent, and obsessive personality, as well as suppressed homosexual tendicies, in which he gets away with due to his place in power.
Harming Sohrab is just another part of his revenge on Hassan, destroying his son as he had destroyed the father, and as their culture believes, is destroying Sohrabs after-life as well as his exsisting life.
This torture of Sohrab just causes a satisfaction in Assef he could not get and finish with Hassen.
I hope that helps a bit