# 1 how many homorphisms are there from Z24 onto Z11how many are th

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1.how many homorphisms are there from Z24 onto Z11?
how many are there to Z11?
what are they?
2.how many homorphisms are there from Z12 onto Z4?
how many are there to Z4?
what are they?
Solution
The number of homomorphisms from Zn to Zm will be
equal to gcd(n,m).
1.Z24 to Z11
gcd(24,11) is 1 therefore the number of homomorphisms
will be 1.
This homomorphism will be the trivial one i.e, all of Z24
mapped to zero of Z11.
2.Z12 to Z4
gcd(12,4) is 4 therefore the number of homomorphisms will
be 4.

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1.how many homorphisms are there from Z24 onto Z11? how many are there to Z11? what are they? 2.how many homorphisms are there from Z12 onto Z4? how many are there to Z4? what are they? Solution The number of homomorphisms from Zn to Zm will be equal to gcd(n,m). 1.Z24 to Z11 gcd(24,11) is 1 therefore the number of homomorphisms will be 1. This homomorphism will be the trivial one i.e, all of Z24 mapped to zero of Z11. 2.Z12 to Z4 gcd(12,4) is 4 therefore the number of homomorphisms will be 4. Name: Description: ...
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