Recent content by Jen917

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.