and because the normal subgroup is abelian i can write the as as you did correct?
No! Read again, very carefully and writing down the proof ina sheet of paper, the proof: in no place he did write anything from where one can deduce the normal sbgp. is abelian which, of course, is false in general...and he didn't write what you say he did.
I guess what I dont understandis how the and get pushed outside.
Heres what I have so far.
We have to show is true. Then, and I can write the thing as then I get stuck
Take and multiply it both from the left and from the right by , and then arrange parentheses accordingly (using associativity) and then use normality of H in G and normality of K in H. That's all the trick.