- #1
zoner7
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Homework Statement
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
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?