Question

How many different homomorphisms o : Z/5ZZ/20Z are there?

Answer 1

Answer:

2

Step-by-step explanation:

We are given that

$O:Z/5Z\rightarrow Z/20Z$

We have to find number of different homomorphisms

We know that

Z/5Z is isomorphic to $Z_5$ and $Z/20Z$ isomorphic to $Z_{20}$

We know that

If $O:Z_n\rightarrow Z_m$

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.