Giles Gardam

activity

20172023

most citedA counterexample to the unit conjecture for group rings

36 citations · 50 across the 10 of their papers we have counts for

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Showing 2021Show all

3 papers · 1 filter

math.GR2021

Algebraically hyperbolic groups

Giles Gardam, Dawid Kielak, Alan D. Logan

We initiate the study of torsion-free algebraically hyperbolic groups; these groups generalise torsion-free hyperbolic groups and are intricately related to groups with no Baumslag…

math.GR2021★ 36 cited

A counterexample to the unit conjecture for group rings

Giles Gardam

The unit conjecture, commonly attributed to Kaplansky, predicts that if $K$ is a field and $G$ is a torsion-free group then the only units of the group ring $K [G]$ are the trivial…

math.GR2021

JSJ decompositions and polytopes for two-generator one-relator groups

Giles Gardam, Dawid Kielak, Alan D. Logan

We provide a direct connection between the Z_{max} (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianis…