A simplified version of the proof was later given by Ernst Witt. Witt's proof is sketched below. Alternatively, the theorem is a consequence of the Skolem–Noether theorem by the following argument. Let "D" be a finite division algebra with center "k". Let ["D" : "k"] = "n"2 and "q" denote the cardinality of "k". Every maximal subfield of "D" has "qn" elements; so they are isomorphic and thus are conjugate by Skolem–Noether. But a finite group (the multiplicative group of "D" in our case) cannot be a union of conjugates of a proper subgroup; hence, "n" = 1.