Is it appropriate to ask a research-level question that is not part of a research problem? I think that the following question is conceivably research-level, but it arose just as a curiosity, not part of any serious research. Is it reasonable to ask it on MO? (I include the specific question in case it affects your answer, but I am not intending to ask the question in this inappropriate forum.) > Suppose that $V_1$ and $V_2$ are vector spaces (over $\mathbb C$, say) with the same underlying set $X$. Suppose that the set of permutations of $X$ that are linear automorphisms of $V_1$ is the same as the analogous set for $V_2$. Then are $V_1$ and $V_2$ isomorphic? EDIT: Stefan Kohl points out that it doesn't matter how the question arose, so probably I should clarify that I was asking because I don't _know_ if a random curiosity is research-level—as opposed to something that arose in my research, which more or less by definition is (hopefully!).

Many people like to know where a problem came from. But don't be afraid to reply that you just had some idea and found it interesting. We mathematicians can identify with that. Of course we might not agree with you on how interesting the problem is, and some of us (not me) will be eager to tell you so.