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Infinite simple characteristic quotients

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arxiv 2312.11684 v3 pith:YJFYZFEY submitted 2023-12-18 math.GR

Rémi Coulon , Francesco Fournier-Facio This is my paper · ORCID
classification math.GR
keywords quotientscharacteristicgroupsinfinitesimpleallowingansweringcertain
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We construct continuum many infinite, simple, characteristic quotients of non-abelian free groups, answering a 1978 question of James Wiegold. The method is very flexible, allowing to impose certain properties on the quotients, to generalize the construction to large classes of groups with hyperbolic features, and to produce quasi-isometrically diverse examples.

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  1. Stability, approximable quotients, and higher property (T)

    math.GR 2025-12 conditional novelty 7.0 of 10

    Every countable (recursively presented) group embeds into a finitely presented, property (T), Frobenius-stable group whose second cohomology is nonzero for every unitary representation.

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