- #1
CornMuffin
- 55
- 5
Homework Statement
Prove: If H is a subgroup with finite index in G
Then there is a normal subgroup K of G such that K is a subgroup of H and K has index less than n! in G.
Homework Equations
Note: |G| represents the index of H in G
|G| is the number of left cosets of H in G, ie # of elements in {gH: g in G}
The Attempt at a Solution
I haven't had much progress in this proof at all.
The only thing that I can think of using is that |G : K| = |G : H||H : K| for a subgroup K of H
But i don't know what to try.