Re: Groups, Magmas, Cayley Tables and Venn Diagrams...

"See the picture placing magmas, quasigroups, semigroups, loops,
monoids, and groups in a lattice of inclusion at the Wikipedia page on
"Magma (algebra)". "

--- Ironically it was precisely this diagram that got me yearning for
a venn diagram instead. The diagram didn't clear things up for me, it
just made me more confused! My difficulty is this: If all these
varying "group-like structures" can all be completely
"represented" (in a loose sense) by a multiplication table then there
must be some sort of venn diagram-esque nesting/intersection of ALL
the different types. All my questions have been asked to clarify this
point... (and you have been most helpful in aiding me to sort it all
out!)

The diagram you advise me to refer to is a good example of my personal
cognitive dissonance in regards to this... It bifurcates instead of
showing how Semi-groups and Quasi-groups are related in the overall
picture. I am sure there is a good reason for it, but it is just
downright confusing for a beginner like myself that is just trying to
get a lay of the land so to speak... See my next post for more...

Thanks!
.

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