What are the finite subgroups (subloops that are groups) of $\mathrm{SL}_2(\mathbb{O})$? In particular, are there any not contained in a $\mathrm{SL}_2(\mathbb{H})$?
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3$\begingroup$ What do you mean by $SL_2({\mathbb O})$? (I know what $SL_2({\mathbb H})$ is.) As far as I know, this object does not exist as a group. $\endgroup$– Moishe KohanCommented Jan 28, 2023 at 23:59
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2$\begingroup$ It is not a group, but it is a loop. $\endgroup$– Daniel SebaldCommented Jan 29, 2023 at 0:19
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1$\begingroup$ I don't think this is a commonly known object, perhaps you could add a definition or at least give a reference where a definition can be read? Depending on that, your Moufang loop may or may not contain $Spin(9,1)$ and/or a group related to $G_2$. Either would then contain finite subgroups not contained in a $SL_2(\mathbb{H})$. $\endgroup$– Max HornCommented Aug 14, 2023 at 6:46
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