Four Group-theoretic Proofs of Wedderburn's Little Theorem
Alan Roche · Irish Mathematical Society Bulletin · 2021
Wedderburn proved in 1905 that a finite division ring is always a field.His result has intrigued generations of mathematicians, spurring generalizations and alternative proofs.The shortest, most elegant proof is surely Witt's from 1931, now the standard textbook treatment.Following a strategy of Zassenhaus, we present four overlapping group-theoretic proofs.The first uses a counting argument; the others hinge on properties of special classes of finite groups.