# Find specific elements with a given order in quotient group

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

• What is your group operation here? Pointwise addition? – enedil Feb 10 at 1:46
• @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. – Midas Hu Feb 10 at 1:55
• 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 $G$. – enedil Feb 10 at 1:57
• @enedil Normal vector addition. – Midas Hu Feb 10 at 2:00
• What is $\mathbb Z v_1 + \mathbb Z v_2 + \mathbb Z v_3$? – enedil Feb 10 at 2:03