I asked this question earlier today and, while I understand it's a somewhat vague and abstract question—it doesn't strike me as unclear. I'd not be surprised if there are some misunderstandings, or a triviality/mixup I'm not seeing, but it's only been downvoted with a vote to close for being "unclear."

What can I do to clarify this question?

  • $\begingroup$ Is your $*$ a mapping $X\times X\to X$ or $X\to X$? If your example is "multiplication by $-1$, then it is the latter interpretation. but then I am not sure what is $h*x$ $\endgroup$ – user99914 Feb 3 '18 at 18:45
  • $\begingroup$ @JohnMa Ah! I see the mistake. What I really meant was the operation $\text{multiplication}$ doesn't have that property if $h, g, x \in \mathbb{Z}$, because one can multiply by $-1$. Does my edit make more sense? $\endgroup$ – AmagicalFishy Feb 3 '18 at 19:07
  • $\begingroup$ I did not understand the second paragraph that much. Everything else was clear though, in my opinion. $\endgroup$ – Mr Pie Feb 3 '18 at 22:43

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