File talk:Algebraic structures - magma to group.svg

At best confusing, at worst wrong

As was pointed out in a former version of this diagramm — https://commons.wikimedia.org/wiki/File_talk:Magma_to_group4.svg – this diagramm is wrong (or at least confusing): this diagramm seems to say that an associative quasigroup is an inverse semigroup. Technically true, but in fact, an associative quasigroup is a group! And not all inverse semigroups are quasigroups. Also, "invertibility" and "divisibility" have different definitions depending on the context, they all agree if there's an identity but not in general, so not all red arrows are the same. I think pages using this version of the diagramm should revert to this version: https://commons.wikimedia.org/wiki/File:Magma_to_group2.svg , and a newer, correct and better labelled version should be created (yes I am working on it). 2A02:8428:4824:7001:F4F9:9CD4:927B:AB67 11:58, 13 October 2022 (UTC)

I have uploaded a corrected version (but for some reason it does not seem to display this latest version; maybe waiting will fix it). Associative quasigoups is slightly broader broader class than groups: since it does not require inverses, and hence the existence of an identity element, the empty quasigroup is in the former and not the latter class. Quondum (talk) 12:43, 28 June 2023 (UTC)