Geodesic
Some Remarks on Groups Admitting a Fixed-Point-Free Automorphism
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1300-1307

Voir la notice de l'article provenant de la source Cambridge University Press

A finite group G is said to be a fixed-point-free-group (an FPF-group) if there exists an automorphism a which fixes only the identity element of G. The principal open question in connection with these groups is whether non-solvable FPF-groups exist. One of the results of the present paper is that if a Sylow p-group of the FPF-group G is the direct product of any number of mutually non-isomorphic cyclic groups, then G has a normal p-complement. As a consequence of this, the conjecture that all FPF-groups are solvable would be true if it were true that every finite simple group has a non-trivial SylowT subgroup of the kind just described. Here it should be noted that all the known simple groups satisfy this property. 
Gross, Fletcher. Some Remarks on Groups Admitting a Fixed-Point-Free Automorphism. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1300-1307. doi: 10.4153/CJM-1968-128-5
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