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How can I deal with the quotient group generated by several element? And how can I find the element with a given order.

  • $\begingroup$ What is your group operation here? Pointwise addition? $\endgroup$ – enedil Feb 10 at 1:46
  • $\begingroup$ @enedil Maybe I hadn’t describe it precisely, I mean, I don’t know the structure of the quotient group mentioned in question, and I also wonder how can I find the elements in the quotient group with order 2. $\endgroup$ – Midas Hu Feb 10 at 1:55
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    $\begingroup$ I mean, if $\mathbb Z^3$ is a group, what operation do you equip it with? So far it has nothing to do with the structure of $G$. $\endgroup$ – enedil Feb 10 at 1:57
  • $\begingroup$ @enedil Normal vector addition. $\endgroup$ – Midas Hu Feb 10 at 2:00
  • $\begingroup$ What is $\mathbb Z v_1 + \mathbb Z v_2 + \mathbb Z v_3$? $\endgroup$ – enedil Feb 10 at 2:03

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