- #1
NanoSaur
- 1
- 0
Suppose A is a finite abelian group and p is a prime. A^p={a^p : a in A} and A_p={x:x^p=1,x in A}.
How to show A/A^p is isomorphic to A_p.
I tried to define a p-power map between A/A^p and A_p and show this map is isomorphism.
But my idea didnot work right now. Please give me some help.
In addition, How to show the number of subgroups of A of order p equals the number of
subgroups of A of index p.
How to show A/A^p is isomorphic to A_p.
I tried to define a p-power map between A/A^p and A_p and show this map is isomorphism.
But my idea didnot work right now. Please give me some help.
In addition, How to show the number of subgroups of A of order p equals the number of
subgroups of A of index p.