On a theorem of Burnside on fixed-point-free automorphisms

On a theorem of Burnside on fixed-point-free automorphisms

. 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...

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Veröffentlicht in:Archiv der Mathematik 2008-02, Vol.90 (2), p.97-100
Hauptverfasser: Deaconescu, Marian, Walls, Gary L.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:. 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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-007-2407-9