Rips-Segev torsion-free groups without the unique product property

DOI10.1016/j.jalgebra.2015.05.004zbMath1402.20046arXiv1307.0981OpenAlexW2167367588MaRDI QIDQ2347997

Markus Steenbock

Publication date: 10 June 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0981

zbMATH Keywords

random groupsunique product groupsgraphical small cancellation groupsKaplansky zero-divisor conjectureRips-Segev groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67) Ordered groups (group-theoretic aspects) (20F60) Cancellation theory of groups; application of van Kampen diagrams (20F06) Probabilistic methods in group theory (20P05)

Related Items (14)

A combination theorem for cubulation in small cancellation theory over free products ⋮ Unique product groups and congruence subgroups ⋮ Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility ⋮ Infinitely presentedC(6)-groups are SQ-universal ⋮ Rips construction without unique product ⋮ Generic algebraic properties in spaces of enumerated groups ⋮ Infinitely presented graphical small cancellation groups are acylindrically hyperbolic ⋮ A new test for asphericity and diagrammatic reducibility of group presentations ⋮ A counterexample to the unit conjecture for group rings ⋮ Negative curvature in graphical small cancellation groups ⋮ Small cancellation theory over Burnside groups ⋮ Subgroups of right-angled Coxeter groups via stallings-like techniques ⋮ Finite index subgroups without unique product in graphical small cancellation groups: Figure 1. ⋮ Coning-off CAT(0) cube complexes

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