I'm currently studying factor groups in abstract algebra and needed some help understanding how to determine the order of an element in a factor group(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have Z (mod 12) / <4>. And I choose some random element from Z (mod 12) such as 5 or 7. How would I go about determining the order of 5 + <4> or 7 + <4> in the factor group. The way I understand is that in Z (mod 12) / <4> we collapse everything in <4> to the identity in Z (mod 12) so that 5 for instance would have order |{5,10,3,8}| = 4 because 8 is an identity in the factor group. Any help or correction on my admittedly poor understanding would be great.

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# Element order in factor groups

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