We prove the Tits alternative for an almost coherent group which is not virtually properly locally cyclic. In particular, we show that an almost coherent 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 , 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 , presque cohérent et qui ne peut pas être engendré par moins de éléments, contient toujours un groupe libre non abélien.
Michel Boileau 1; Steven Boyer 2

@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/} }
TY - JOUR AU - Michel Boileau AU - Steven Boyer TI - On the Tits alternative for $\protect \mathit{PD}(3)$ groups JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 397 EP - 415 VL - 28 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1604/ DO - 10.5802/afst.1604 LA - en ID - AFST_2019_6_28_3_397_0 ER -
%0 Journal Article %A Michel Boileau %A Steven Boyer %T On the Tits alternative for $\protect \mathit{PD}(3)$ groups %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 397-415 %V 28 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1604/ %R 10.5802/afst.1604 %G en %F AFST_2019_6_28_3_397_0
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 spécial en l’honneur de Jean-Pierre OTAL “Low dimensional topology, hyperbolic manifolds and spectral geometry”, 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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