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Infinite simple characteristic quotients
[Quotients caractéristiques simples infinis]
Rémi Coulon1 ; Francesco Fournier-Facio2
1Université Bourgogne Europe, CNRS, IMB UMR 5584, 21000 Dijon, France
2Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 1463-1481

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.

Nous construisons un continu de quotients caractéristiques simples infinis de groupes libres non abéliens, répondant ainsi à une question posée par James Wiegold en 1978. La méthode est très flexible et nous permet d’imposer des propriétés remarquables à ces quotients, de généraliser la construction à de larges classes de groupes ayant une forme de courbure négative, et de produire une grande diversité d’exemples qui, deux à deux, ne sont pas quasi-isométriques.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.352
Classification : 20E32, 20E36, 20F06, 20F65, 20F67
Keywords: Simple groups, characteristic groups, Wiegold conjecture, small cancellation theory
Mots-clés : Groupes simples, groupes caractéristiques, conjecture de Wiegold, théorie de la petite simplification

Rémi Coulon  1   ; Francesco Fournier-Facio  2

1 Université Bourgogne Europe, CNRS, IMB UMR 5584, 21000 Dijon, France
2 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Rémi Coulon; Francesco Fournier-Facio. Infinite simple characteristic quotients. Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 1463-1481. doi: 10.5802/jep.352
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