Should we have a tag for (quotient-groups)?

Question

I think that quotient groups are relatively important topic and we certainly have some questions about them. We do have tags for normal-subgroups and for quotient-spaces. As far as the importance of the topic and frequency of questions asked here on MSE are concerned, I'd say that these concepts are comparable.

Should we introduce the tag quotient-groups?

Quotient groups and normal subgroups are very closely related topics. So maybe other reasonable way to go would be to have them in the same tag. (In this case I think the base way to proceed would be to create the tag quotient-groups and make the two tags synonymous. Creating the tag synonym would mean that if someone starts typing quotient in the tags field, the tag (quotient-groups) is offered to them as one of the possibilities.) Of course, if we have both topics in the same tag, it should be mentioned also in the tag-info. At the moment the tag-excerpt and the tag-wiki for (normal-subgroups) are rather short. But since the content of the tag seems to be clear from the name of the tag, I do not think that this is a problem.

Would it be better to have these two topics in the same tag? (So that we do not create too many tags.)

Answer 1

I honestly think that a tag like this will be used quite inconsistently (e.g., not used in questions that are certainly about quotient groups, and used in cases when the concept of quotient groups appears only incidentally in the question). As such, I am uncertain about the value of having this tag. (That a question has this tag only means that "quotient groups" is somehow related to the question, but it would not indicate that the focus of the question is on the concept itself (e.g., I can envision a question like "How many generators does $\mathbb{Z}/n\mathbb{Z}$ have?" being tagged quotient-groups, but I don't really feel that its use in this case would be warranted). Also, the exclusion of the tag wouldn't say anything at all about whether it is about quotient groups.)

Incidentally, I think that the normal-subgroups tag — among many others — has a similar problem. (For example, this question is certainly about normal subgroups, but is currently not so tagged. At the same time I have no idea why this question is deemed to be about normal subgroups.)

You can say that this is an editing problem, but the simple fact is that the vast majority of active users don't edit (and I largely consider myself part of this problem). As of the latest data dump to the SEDE, only 1701 questions posted this month so far have had their tags edited (SEDE query), which is less than three days worth of questions at our current rate. I highly doubt that 80% of our questions are given fully appropriate tags in their first revision. (As a point of comparison, of the 1196 questions posted to physics.SE so far this month — according to the SEDE — 754 have had their tags edited at least once.)

_{(Sorry about this little rant.)}