Can anyone come up with an example of a group of order 4 that has no order 4 elements? I have tried a few examples I learned in class but I couldn't come up with this particular one.
Example of a Group
-3
$\begingroup$
abstract-algebra
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0Might I ask what some of the examples were that you tried? – 2017-02-04
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0Hint: There are only two groups of order four. – 2017-02-05
1 Answers
2
$\mathbb{Z}_2 \times \mathbb{Z}_2.$
$(0,1),(1,0)$ and $(1,1)$ have order $2.$ $(0,0)$ is the identity.
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0Ah this. Thank you, I can confirm. – 2017-02-04