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I have just learned about cosets and meet with the following question.

Find all left cosets of the subgroup generated by $\overline a$ in $\mathbb Z_{12}$. I know $\mathbb Z_{12} = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$. I would like to know (for example if $a=2$). What does $\overline a$ mean here? Thanks.

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    Do you want to know how to find the cosets? Or are you just confused about the notation?2011-12-18
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    yes am confused with the notation2011-12-18
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    I see. It seems like Brad's answer should clear things up, then. Just a note: later on you'll learn that $\mathbf Z_{12}$ is the (quotient) group formed by the cosets of $12\mathbf Z$ in the group $\mathbf Z$, so you're looking at cosets of cosets here!2011-12-18

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