A new proof of Zassenhaus theorem on finite groups of fixed-point-free automorphisms

In 1935 H. Zassenhaus [Abh. Math. Semin. Hamb. Univ. 11 (1935) 187–220] stated that a non-trivial finite perfect group of fixed-point-free automorphisms of an abelian group is isomorphic to SL2(5). The paper contains a character-free proof of this theorem.