7 papers · 1 filter
Localizing the Gardam unit: the support geometry of units in F_2[P] and its non-unique-product relatives
Moe Tabei
Gardam's counterexample to the Kaplansky unit conjecture is a unit of , the Promislow group, with support of size ; Gardam asked whether is least poss…
The quantitative non-unique-product landscape at the global minimum: the Nielsen-Soelberg groups
Moe Tabei
Nielsen and Soelberg proved that a finite subset of a torsion-free group with having no unique product satisfies , and exhibited two groups, here and…
The domain question for the Nielsen-Soelberg group rings: the commutative case, with certified ball checks
Moe Tabei
Nielsen and Soelberg exhibited three torsion-free groups G_1, G_2, G_3 carrying 8-element sets without unique products, and asked whether any of the group rings R[G_i], R a domain,…
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…
A compactness theorem for twisted-unitary elements of integral group rings, with a certified route to the theta-unitary Case A at window B(4) of the Promislow group
Moe Tabei
Let G be a torsion-free group whose real group algebra R[G] has no zero divisors, and let u -> u^{*theta} be an l2-isometric anti-involution of R[G] (a composition of the inversion…
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…
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 group of dimension 3, which underlies Promislow's non-unique-product set and Gardam's counterexample to the unit conjec…