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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