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

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.

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.

Publié le :
DOI : https://doi.org/10.5802/afst.1604
@article{AFST_2019_6_28_3_397_0,
     author = {Michel Boileau and Steven Boyer},
     title = {On the {Tits} alternative for $\protect \mathit{PD}(3)$ groups},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {397--415},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {3},
     year = {2019},
     doi = {10.5802/afst.1604},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1604/}
}
Michel Boileau; Steven Boyer. On the Tits alternative for $\protect \mathit{PD}(3)$ groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 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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