On the Tits alternative for PD(3) groups

Michel Boileau (1) , Steven Boyer (2)

1 I2M - Institut de Mathématiques de Marseille
2 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]

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 fewer than four elements always contains a rank 2 free group.

Domaines: Mathématiques [math]

Michel Boileau, Steven Boyer. On the Tits alternative for PD(3) groups. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2019, 28 (3), pp.397-415. ⟨hal-02099184⟩