Abstract.
We prove that a finite group having a fixed-point-free automorphism in the Fitting subgroup of its automorphism group must be abelian of rather restricted structure. As a consequence, no finite nonabelian group could have a fixed-point-free automorphism in the Frattini subgroup of its automorphism group.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 21 April 2007, Revised: 18 May 2007
Rights and permissions
About this article
Cite this article
Deaconescu, M., Walls, G.L. On a theorem of Burnside on fixed-point-free automorphisms. Arch. Math. 90, 97–100 (2008). https://doi.org/10.1007/s00013-007-2407-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-007-2407-9