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I just thought of this idea. I am currently studying some advanced abstract algebra and recently I learned about Jordan-Holder factors, central simple algebras and stuff. The concepts are very new and very abstract to me. And I want to find some examples or exercises to help me understand them. Textbook exercise has the problem of being too "typical". So I was wondering if it is okay to ask for an exercise or an example here. Such questions do risk being off-topic because it is hard to tell what exercise the asker is looking for and what answers should be deemed good answers. Any suggestions?

For example, what I had in mind was:

I want to know more about how to compute Jordan-Holder factors. Can you give me an exercise other than $\mathbb Z/p^n\mathbb Z$ (which is a typical example/exercise used in textbooks)?

To me this seems a bit off-topic as it may be unclear about exactly what kind of examples I am asking for. What additional infomation would be necessary for this to be acceptable on MSE?

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    $\begingroup$ reference request and terminology tags exist. $\endgroup$ – Roddy MacPhee Dec 24 '19 at 15:45
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    $\begingroup$ @RoddyMacPhee I don't know. Does this count as a reference? $\endgroup$ – trisct Dec 25 '19 at 3:04
  • $\begingroup$ Shaum's outlines is available as a set of books at my central library for example. $\endgroup$ – Roddy MacPhee Dec 25 '19 at 3:07
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    $\begingroup$ One thing you can do, in this instance, which helps you grow mathematically is to choose a group yourself. Maybe it's an interesting example, maybe not. But choosing a group yourself, instead of being given one, helps grow your independence in doing math. You want a group, choose one and compute; don't wait on someone else. Don't be afraid to choose more complicated groups than cyclic groups or abelian groups. Can't think of any groups besides basic cyclic groups? Then this is a learning opportunity in itself. $\endgroup$ – Al Jebr Dec 28 '19 at 22:59
  • $\begingroup$ I vote to try it using the correct tabs - either you will get voted down or you will get good answers $\endgroup$ – Burt Dec 29 '19 at 4:53
  • $\begingroup$ To me this seems like a (more on-topic than usual) application of big-list $\endgroup$ – Alexander Gruber Dec 29 '19 at 17:35
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    $\begingroup$ Note that outside the context of a classroom an exercise is usually called an application. And questions about applications are well-received here :) $\endgroup$ – Taladris Jan 2 at 16:45
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A cursory search shows that such questions have been well-received in the past: Posts containing "exercises". As Roddy MacPhee suggests, almost all of these use the reference-request tag. It seems that the community tacitly approves. I like the idea as well.

A successful "exercises" question seems to be "give me a place to find exercises," not just "give me some exercises." (Notable exception: Yoneda Lemma Exercises.) For many subjects this is probably more fruitful, and likelier to be received well.

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