Proving H is normal

1. Oct 31, 2008

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...

2. Oct 31, 2008

Office_Shredder

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

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

3. Oct 31, 2008

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.