This was my idea:
K is a nonempty set and has an identity element, we know this because it is a subgroup of H.
K also contains the inverse of an element following the same logic.
Finally we know K is closed because it is a subgroup of H.
H is a subgroup of G, therefore K has all these...
Let H be a subgroup of G and let L be a subgroup of H. Prove that K is a subgroup of G.
This question seems very redundant to me, isn't anything in a subgroup automatically a subgroup of anything the larger group is a subgroup of. Can some one explain this proof to me?
Let G be a group and let H be a subgroup.
Define N(H)={x∈G|xhx-1 ∈H for all h∈H}. Show that N(H) is a subgroup of G which contains H.
To be a subgroup I know N(H) must close over the operations and the inverse, but I am not sure hot to show that in this case.