I was doing a course on algebra and had this question written in my notes.
Prove that if H is a normal subgroup of G and K is a normal subgroup of H, then K may not be a normal subgroup of G.
Now as I understand to prove a subgroup K normal to G I have to do g^(-1)kg belongs to K. Clearly, This equation will be satisfied for all g belonging to H (as K is a normal subgroup to H) but not necessarily for g belonging to G-H.
Formally, I am at a loss how to show this that there may exist an element which will not satisfy this. Moreover I feel I am missing something as I have still not used H is a subgr