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June 21, 2026Journal of AlgebraOpen Access

Uncountably many quasi-isometric torsion-free groups

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The aim is to demonstrate the existence of uncountably many finitely generated, pairwise non-isomorphic torsion-free groups within the same quasi-isometry class.
Utilized Schur covering groups to define group structures.
Applied principles of group cohomology to analyze properties.
Incorporated bounded-valued cohomology for geometric insights.
Constructed uncountably many pairwise non-isomorphic torsion-free groups.
All constructed groups belong to the same quasi-isometry class.
Demonstrated new relationships among finitely generated groups through cohomological methods.

Implication

We construct uncountably many finitely generated torsion-free groups indicating new insights into group class structures.

Abstract

We construct uncountably many finitely generated, pairwise non-isomorphic torsion-free groups, all of which fall into the same quasi-isometry class. This is done by considering Schur covering groups and group cohomology, with the necessary geometric ingredient coming from the theory of bounded-valued cohomology.

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Cite This Study

Vladimir Vankov (2026) studied this question.

synapsesocial.com/papers/6a377fdd24f042ddf4c5a277 https://doi.org/10.1016/j.jalgebra.2026.06.013

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Implication

We construct uncountably many finitely generated torsion-free groups indicating new insights into group class structures.

Uncountably many quasi-isometric torsion-free groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Uncountably many quasi-isometric torsion-free groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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