**Bielefeld-Münster Seminar**

Date: 22 Feburary 2017

Venue: Bielefeld University

All talks will take place in V3-201. Coffee will be served in the same room during the breaks.

If you have questions, please contact the organizer.

### Schedule

10:00 Uhr | Yuri Santos |

Finite presentability of parabolics in Chevalley groups | |

11:00 Uhr | Coffee break |

11:30 Uhr | Eduard Schesler |

Bounded subgroups of relatively finitely presented groups | |

12:30 Uhr | Lunch break |

14:00 Uhr | Cora Welsch |

Contractibility of coset posets of finite index subgroups of finitely generated infinite groups | |

15:00 Uhr | Coffee break |

15:30 Uhr | Nils Leder |

Automorphisms of Free Products and Property (FA) | |

16:30 Uhr | End the of seminar |

### Abstracts

#### Yuri Santos

*Finite presentability of parabolics in Chevalley groups*

Given a parabolic subgroup P = UL of a universal Chevalley group, we consider the question of how do presentations of P and of its Levi factor L relate. We shall obtain a criterion, based on the underlying root system, to determine a "nice" relative presentation of P with respect to L via generators and relators à la Steinberg. Invoking results of Behr, Bux and others, we are able to classify finitely presentable S-arithmetic subgroups of parabolics of almost simple algebraic groups in many new cases.

#### Eduard Schesler

*Bounded subgroups of relatively finitely presented groups*

We begin by introducing relatively finitely presented groups which generalize relatively hyperbolic groups. Since a relatively finitely presented group G is equipped with a generating set X which may contain infinite parabolic subgroups, it makes sense to study infinite bounded subgroups of G. We will show that every infinite bounded subgroup of G is already conjugated into a parabolic subgroup if the relative Dehn function of G is well defined.

#### Cora Welsch

*Contractibility of coset posets of finite index subgroups of finitely generated infinite groups*

I have proved that the nerve and the order complexes of the poset of the coset of all finite index subgroups are contractible for many important classes of finitely generated infinite groups. Thus the upcoming question was: Are there groups such that the nerve and order complexes are not contractible? We can now answer this question in the affirmative and give examples.

#### Nils Leder

*Automorphisms of Free Products and Property (FA)*

A group H is said to have Serre's property (FA) if any action of H on a tree T has a global fix point, i.e. there is a vertex v ∈ V(T) such that h(v)=v holds for all h ∈ H.

Let n, m ∈ ℕ,n,m ≥ 2 and G=ℤ/nℤ * … * ℤ/nℤ denote the free product of m copies of the finite cyclic group ℤ/nℤ. I am interested in the question wether the automorphism group Aut(G) has property (FA).

In order to explore the structure of Aut(G), we consider so called

In particular, this implies that Aut(G) does not have property (FA) in the case of m=2 free factors.