Recent content by sukyung

For example, H: Z_12 -> Z_5 and Z_12 is a cyclic group but it cannot create a homorphism to Z_5 by specifying H(1). Then Can I understand it as "we can create a homomorphism by defining each H(1) when the homomorphism is an endomorphism on a cyclic group(like Z)"?

Denote Z_n=(0.1.2...n-1) Then could I generalize the number of homomorphism H:Z_n -> Z_m as gcd(n, m)=#(H:Z_n -> Z_m) ? (Don't consider the case H:Z -> Z) For example #(H: Z_4 -> Z_2)=2 #(H: Z_12 -> Z_5)= 1 (obviously the trivial one)

oh Obviously there are infinitely many homomorphisms on Z to Z But could you suggest the number more precisely by using cardinal numbers?