Counting the number of homorphisms

  • Thread starter seshikanth
  • Start date
  • #1
20
0

Homework Statement


Hi,
I am trying to solve the following question:
count the number of homomorphism between Z/mZ and Z/nZ?
Can you tell me is my solution correct?


Homework Equations





The Attempt at a Solution


Let f be a homorphism.
f(mZ + a) = nZ + b ; a,b belong to G
Now, o(nZ+b) | n (from lagrangian theorem)
o(f(mZ+a)) = o(nZ+b); and o(f(mZ+a)) | o(mZ+a) which implies o(nZ+b) | m
Number of possiblities for o(nZ+b) = Number of common factors for m and n = Eulers Quotient for gcd(m,n)

Can you tell me if the approach correct? Because when i check the answers of the exercise question it is gcd(m,n) but here i am getting Euler's Qutient for gcd(m.n) = [tex]\varphi(gcd(m,n))[/tex]

Thanks,

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

Related Threads on Counting the number of homorphisms

Replies
1
Views
719
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
4
Views
750
Replies
4
Views
434
Replies
6
Views
6K
  • Last Post
Replies
6
Views
2K
Replies
6
Views
1K
  • Last Post
Replies
1
Views
1K
Top