# Order of Elements, Factor Groups and Homomorphisms

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 ...

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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.