origins of Wedderburn’s theorem

Wedderburn and Dickson both published independent proofs of the fact in 1905.Wedderburn’s publication contains three proofs, the first of which was ultimately flawed. The second two proofs improve the essential trick of Dickson by using Zsigmondy’s theorem, a numerical condition on prime factors of $p^n-1$. Wedderburn and Dickson were colleagues at the University of Chicago at the time.

The first, mistaken proof, of Wedderburn was later corrected and simplified by Artin and is now the standard proof in most texts.