The Fitting subgroup of a Frobenius group is its kernel.
Any hints, suggested books or papers for the proof?
2026-02-23 08:24:59.1771835099
The Fitting subgroup of a Frobenius group
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This follows from the deep result of John Thompson that the kernel of a finite Frobenius group is nilpotent. Equivalently, a finite group that admits a fixed-point-free automorphism of prime order is nilpotent.
The original reference is: Thompson, John G. (1960), "Normal p-complements for finite groups", Mathematische Zeitschrift, 72: 332–354.
There is also a complete proof in the book "Permutation Groups" by D. Passman.