New Examples of Torsion-Free Non-unique Product Groups

2013/02/01 by William Carter, Carter, William
Mathematics · #20C07 (secondary) #20F05 (primary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20C07 #msc:20F05

paper · pdf · doi:10.48550/arxiv.1302.0049

Incorporates referee's suggestions, updated references

arxiv created 2013/11/24 · arxiv updated 2013/11/26

Abstract

We give an infinite family of torsion-free groups that do not satisfy the unique product property. For these examples, we also show that each group contains arbitrarily large sets whose square has no uniquely represented element.

Related

• Unique product groups and congruence subgroups
• Cardinality of product sets in torsion-free groups and applications in group algebras
• Uncountably many quasi-isometric torsion-free groups
• Non-amenable finitely presented torsion-by-cyclic groups
• Constructions of torsion-free countable, amenable, weakly mixing groups