Deloro–Wiscons conjecture on ranked quasi-Frobenius groups of odd type

Let GG and CC be ranked connected groups such that C<GC<G, [NG(C):C]<\finite[N_G(C):C]<\finite, and CCg={1}C\cap C^g=\{1\} for every gNG(C)g\notin N_G(C). Suppose that C<GC<G is a ranked quasi-Frobenius group of odd type, meaning that it contains involutions and is U2U_2^{\perp}. Deloro–Wiscons conjecture.

  • If [NG(C):C]=2[N_G(C):C]=2, then GPGL(2,K)G\simeq \operatorname{PGL}(2,K) for KK an algebraically closed field of characteristic other than 22.
  • If [NG(C):C]=1[N_G(C):C]=1, then GG is split and solvable.

This conjecture proposes a classification of ranked quasi-Frobenius groups of odd type, distinguishing the degree-two case from the Frobenius case. The supplied source does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

Samuel Zamour, “Ranked definably linear quasi-Frobenius groups”, arXiv:2403.04375 (2025).

Additional references

2 papers in this index state this conjecture (2022–2024). The statement above is taken from the most recent of them; the others are arXiv:2204.02652.

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