On the Tits alternative for PD(3) groups
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 397-415.

We prove the Tits alternative for an almost coherent PD(3) group which is not virtually properly locally cyclic. In particular, we show that an almost coherent PD(3) group which cannot be generated by less than four elements always contains a rank 2 free group.

On montre qu’un groupe à dualité de Poincaré de dimension 3, presque cohérent et tel que tout sous-groupe d’indice fini contienne un sous-groupe propre de type fini non cyclique, vérifie l’alternative de Tits. On obtient en particulier qu’un groupe à dualité de Poincaré de dimension 3, presque cohérent et qui ne peut pas être engendré par moins de 4 éléments, contient toujours un groupe libre non abélien.

Published online:
DOI: 10.5802/afst.1604

Michel Boileau 1; Steven Boyer 2

1 Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France
2 Département de Mathématiques, Université du Québec à Montréal, 201 avenue du Président-Kennedy, Montréal, QC H2X 3Y7, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Michel Boileau; Steven Boyer. On the Tits alternative for $\protect \mathit{PD}(3)$ groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 3, pp. 397-415. doi : 10.5802/afst.1604. https://afst.centre-mersenne.org/articles/10.5802/afst.1604/

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