{"id":"palomar/PALOMAR-2026-09-27-000006","url":"https://github.com/yawara/peterfalvi-problem/tree/698b7ae0af649f7fad48c482aa8ff0d2d14336bb","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-27-000006-v1.json","repo":"https://github.com/yawara/peterfalvi-problem","tags":["math.GR","math.NT","msc:20D05","msc:20D10","msc:11T06","group-theory","finite-groups","combinatorics"],"score":0,"title":"Péterfalvi's Problem for p = 3: No Group Satisfies Hypothesis (B)","trust":"high","domain":"math.GR","source":"palomar","authors":["Yawara Ishida"],"reviews":0,"subject":"math.GR","summary":"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.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true}