Péterfalvi's Problem for p = 3: No Group Satisfies Hypothesis (B)
Glauberman and Norton (Proc. Amer. Math. Soc. 119, 1993) end their paper on a combinatorial problem that arises in the proof of the Feit–Thompson odd order theorem with a question of Péterfalvi: can the hypothesis of their Proposition 9 be satisfied for p = 3? The same question is Problem 1 in Appendix C of Bender and Glauberman, Local Analysis for the Odd Order Theorem (1994). Let F be the field with p^q elements, P its additive group, U its group of units of norm one over the prime field, H the semidirect product P ⋊ U, and P₀ the image of the additive group of the prime field in H.…
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