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There are several proofs of the famous classification of finite subgroups of $SO(3)$. I heard that there is a "purely algebraic" one attributed to Camille Jordan. Does anybody know of a reference?

Thanks!

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There's an old book by H.F. Blichfeldt called "Finite Collineation Groups" (University of Chicago Press, 1917 I believe) which deals with the classification of finite linear groups in low dimensions, and which has some historic interest.There is another book by (G.A) Miller, (H.F) Blichfeldt and (L.E.) Dickson frm around the same period. Following that,there was quite a long gap before the finite subgroups of ${\rm GL}(5,\mathbb{C})$ were classified (by R. Brauer, using algebraic means, including modular representation theory) in the mid 1960s, and several students of Brauer and also of W. Feit, treated higher dimensional groups in subsequent years.

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  • $\begingroup$ Emmanuel Breuillard wrote some time ago (see here math.u-psud.fr/~breuilla/Jordan.pdf) a short text on Jordan's theorem that might be worth reading. $\endgroup$
    – Matheus
    Commented Nov 15, 2012 at 18:03

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