Answer:
2
Step-by-step explanation:
We are given that
[tex]O:Z/5Z\rightarrow Z/20Z[/tex]
We have to find number of different homomorphisms
We know that
Z/5Z is isomorphic to [tex]Z_5[/tex] and [tex]Z/20Z[/tex] isomorphic to [tex]Z_{20}[/tex]
We know that
If [tex]O:Z_n\rightarrow Z_m[/tex]
Number of homomorphism=gcd(m,n)
Gcd(5,10)=2
5 does not divide by 20 therefore, there are no onto homomorphisms.
There are only two homomorphisms.
