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It seems like there are a decent number of questions about placing some sort of order on a group. I would like to tag these questions to better organize them, but I'm not sure what to call the tag.

The phrase "ordered group" to me implies that we have a total order $\leq$ which is preserved under both left and right multiplication. But people could be asking questions about partial or lattice orders, or the ordering could be preserved only under right multiplication, etc.

Creating separate tags for each of these niche subjects seems like overkill to me, so is the standard to just call it [ordered-groups] and assume people will be able to figure out the ambiguity? One alternative would be to call it [partially-ordered-groups] and hope that people realize that even if they have a stronger restriction, they can still use the tag.

Examples:

(These were taken by searching for questions tagged as both [group-theory] and [order-theory]. I filtered out the ones asking about the order of a group.)

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    $\begingroup$ There is also a possibility to create two tags and make them synonyms. $\endgroup$ – Martin Sleziak Sep 19 '14 at 17:46
  • $\begingroup$ Maybe provide a list of questions (with links) that you feel should use this tag. It would certainly help in ascertaining the viability of the tag. (Also, what would fall under the tag? Clearly not every question about the real line would, but what would the boundaries of the tag be?) $\endgroup$ – user642796 Sep 19 '14 at 18:46
  • $\begingroup$ Thanks, I added some examples. @Arthur: it seems to me that if it's appropriate to add the [group-theory] tag and you care about an ordering, the [ordered-group] tag would apply. $\endgroup$ – Xodarap Sep 19 '14 at 20:16
  • $\begingroup$ "I filtered out the ones asking about the order of a group." -- if [ordered-groups] exists, it will be applied to such questions too. Just a warning. $\endgroup$ – user147263 Sep 19 '14 at 23:26
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    $\begingroup$ Thanks for creating tag-excerpt and tag-wiki. (There are many users who do not bother to do that when creating a new tag.) If you plan to add the tag to some of the examples you listed in your post, keep in mind not to do too many retags in a short timespan. $\endgroup$ – Martin Sleziak Sep 21 '14 at 7:29

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