Well, both of them naively answer this issue. I'd like the OP to know that: "If $G/H$ and $G/K$ are two quotient groups, then, there is a homomorphism between them if and only if $K \subseteq H$" but I am too lazy to get the commutative diagram and write out those proofs.
@tb Thank You for the links. I'll read through and try to understand the second one esp.
@KannappanSampath well, it doesn't take more than a line... Careful with the phrasing though. The quotient map $G \to G/H$ factors over $G \to G/K$ if and only if $K \subset H$. On the other hand, it's in every basic algebra text...
For instance DF gives this "factors through" as more of a notation while he proves these details about the commutativity of the triangle in his Isomorphisms theorem. Am I missing something @tb?
@Ilya We're taking turns. Each one picks truth or dare. If truth the other one can ask a question and the person asked has to reply with the truth. If dare the other one can order them to do something.
Nothing deep, but if the OP is new to this subject, I'd be scaring him/her and that is exactly what I do not want to be doing. (s)he is making very good mistakes!
@RajeshD if you think that a person care about 20-30 stuff, then your phrase won't make him happy anyway. If you think that a person don't care, then there is no need for such phrase. That's my opinion
@MattN so? or you can send me an e-mail. I'll answer you here or there. Just tell me when you send it.
If we have a finite degree extension L over the reals then L is algebraic over the reals so that it is certainly algebraic over the complex numbers. Hence $L = \mathbb{C}$
@AsafKaragila Holy, you are entrusted with passing 150 people? I would very cleverly manipulate and give them points! Why fail them and unnecessarily see them suffer!
@KannappanSampath I am very merciful as a grader. If one of the other guys would have graded this they all would have failed again... he would have given almost everyone <10 points out of 25; I gave many people much more than they deserve in mathematical standards.
@MattN: listen, he doesn't answer. I would suggest attacking him together whenever he will write any message and disprove his absence - in the meanwhile we proceed with our game.
@MattN: and overall, I am not sure I would like to play in this game with him. Before he was always answering my questions whenever I felt interested in this or that part of his life.
@RajeshD You have obviously never graded exams of a theoretical course before. This is how things are in mathematics, inaccurate and approximate. They are not exact and absolute.
@Ilya I'll answer one question for truth by both you and Matt. I can't join in for real though because I gotta go soon. And no, Rajesh, I'm not jobless.
