Fifth dimension subgroups: D₅ = γ₅ when G/γ₂ is finite of exponent 3, candidates for a counterexample, and a reduction of Kourovka 20.84
Lean 4 / Mathlib formalization accompanying S. Vorobev, "On the inclusion D_5(G) ⊆ γ_4(G): reductions, the Lie-ring proof, and evidence" (preprint, 2026; submitted to arXiv math.GR on 2026-10-22). The integral dimension subgroups D_n(G) = {g ∈ G : g − 1 ∈ Δ(G)^n} are defined from the augmentation ideal of Mathlib's integral group ring. Kourovka Problem 20.84 asks whether D_5(G) ⊆ γ_4(G) for every group; it is open and is not claimed here. Unconditional results: D_5(G) = γ_5(G) whenever G/γ_2(G) is finite of exponent 3, and more generally whenever G/γ_2(G) is a finite 3-group whose cubes form…
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