2026/08/04 by Moe Tabei
Mathematics · #math.GR #msc:16S34 #msc:20C07 #msc:68V15
9 pages. Ancillary files: all verification scripts, logs and witnesses (24 files)
arxiv created 2026/08/04 · arxiv updated 2026/08/05
Higman's conjecture that Z[G] has only trivial units, for G torsion-free, is open for the Promislow (Hantzsche-Wendt) group P, the group over which Gardam disproved the field-coefficient unit conjecture in 2021. We introduce an exact reduction of the integral conjecture for P modulo 2 into two sub-problems, record the base cases as consequences of the Craven-Pappas small-length theorems, and argue that the frontier of the integral problem is word-radius 4: a triviality theorem for Z[P] there would be the first statement separating Z from every field. Throughout, claims are ball-limited and stated as such; we make no claim on the full conjecture.