Frobenius conjecture

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There is another conjecture named after Frobenius called the Frobenius conjecture on nth roots. That conjecture is still open.

Statement

The Frobenius conjecture has the following equivalent formulations:

The Frobenius conjecture has been proved by Thompson in his paper Finite groups with fixed-point-free automorphisms of prime order.

References

  • Normal p-complements for finite groups by John G. Thompson, Math. Zeitschr. 72, 332--354 (1960)
  • Finite groups with fixed-point-free automorphisms of prime order by John G. Thompson, Proc. Nat. Acad. Sci. 45, 578-581 (1959)