Proving Normalcy of H in Finite Group G

[joecoz88]

I have been struggling with this proof:

If G is a finite group with exactly one subgroup H of a given order, then H is normal.

I'm not sure where to start...

 

[Office_Shredder]

What can you say about xHx^-1 for any x in G?

You only need to write down the definitions and it becomes obvious

 

[BryanP]

What can you say about the left and right cosets of H in G? Do they coincide under those conditions?

Once you can establish that, it is trivial.