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# Order of Elements, Factor Groups and Homomorphisms

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Help with this linear transformation problem. Please help with the following problem. Provide step by step calculations.

A. What is the order of the element 14 + <8> in the factor group Z24 / <8>?

I know that if I let G = Z24 and H = <8> , then H = <8> = {0,8,16}.
So Z24/<8> = {0+H,1+H,2+H,3+H,4+H,5+H,6+H,7+H}.

b. Prove or disprove: The map x --> 3x is a homomorphism from Z4 to Z6 .

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a. What is the order of the element 14 + in the factor group ?

I know that if I let G = and H = , then H = = . So = . However I'm not sure
what the order of 14 + is. I can't figure out what its ...

#### Solution Summary

Order of Elements, Factor Groups and Homomorphisms are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question. Step by step calculations are given.

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