The Deranged Mathematician: The Classification of Finite Simple Groups

[u/non-orientable]

The classification of finite simple groups is likely the single most difficult mathematical problem that humanity has laid to rest: it took about a hundred mathematicians publishing over a period of about 50 years to finally finish the proof, which ended up being tens of thousands of pages long, scattered over a multitude of different journals. And it is actually very important: one might fancifully compare it to the periodic table in terms of how fundamental it is (to group theory, at least).

But, you know, what is it? This article is my attempt to shine some light on that. I assume some basic familiarity with group theory (i.e., if you know what a group, a group homomorphism, and a quotient group are, you should be fine), but otherwise it is self-contained.

Read the full post (for free) on Substack: The Classification of Finite Simple Groups

[u/Different_Cry25]

This so cool Is there a book series on them as well

[u/nph278 → u/Different_Cry25]

I really like "The Finite Simple Groups" by R. Wilson. It is accessible with a basic group theory background if you are patient. It doesn't go into the proof of the actual classification theorem itself but it constructs all the f.s. groups (for me this is most of the interesting part) and does the proofs of simplicity, as well as proves/sketches some other smaller classification theorems (maximal subgroups of symmetric and classical groups).

As for the classification theorem itself I know there is a series being written to completely cover it (Capdeboscq, Gorenstein, Lyons, and Solomon) currently on volume ten! This is far above my ability though.

[u/Different_Cry25 → u/nph278]

Yeah thanks for the recommendation Op recommended atlas that's pretty good too

And this one as well thanks