(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume that the nonzero elements of Z13 form a group G under multiplication [a]= [ab].

a) List the elements of the subgroup <[4]> of G, and state its order

3. The attempt at a solution

So I thought this would be like some of the previous problems.

I assumed that i was simply asked to keep adding 4 and writing down the values until the value reached 0.

The process would follow as such:

[4] [8] [12] [3] [7] [11] [2] [6] [10] [1] [5] [9] [0]

After placing these elements in order, I would say that the subgroup is of order 13.

My intuition is clearly wrong, because the answer in the back of the book reads:

{[1],[3],[4],[9],[10],[12]} o(<[4]>) = 6

How in the world do they get this answer?

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# Homework Help: More subgroups

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