Moe Tabei

collaborators

4 papers

math.GR2026

Higman in balls: the mod-2 dichotomy for integral units of the Promislow group

Moe Tabei

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-coeff…

math.GR2026

The one-sided unit count of F_2[P] at radius four, and an integral separation theorem

Moe Tabei

Let P be the Hantzsche-Wendt (Promislow) group and B(4) the radius-four ball in its standard word metric. Dietrich, Lee, Nies and Vinyals determined the two-sided count: exactly 36…

math.GR2026

The quantitative non-unique-product landscape at the global minimum: the Nielsen-Soelberg groups

Moe Tabei

Nielsen and Soelberg proved that a finite subset $A$ of a torsion-free group with $A \cdot A$ having no unique product satisfies $∣ A ∣ \geq 8$ , and exhibited two groups, here $G_{1}$ and…

math.GR2026

Least sizes of non-unique-product sets: the Promislow group and a Heisenberg-type candidate

Moe Tabei

Let P be the Promislow group, the orientable Hantzsche-Wendt Bieberbach group of dimension 3, which underlies Promislow's classical non-unique-product set and Gardam's disproof of…