Tea Seminar of our groupPlace and time:

Inhalt:
In this seminar, guests and members of our group present their research, or topics of interest to us. Presently we use a hybrid format for the seminar (inperson and zoom). In case you are interested, please contact Linus Kramer.
Talks:
 08.01.2024 Marjory Mwanza (Münster) On the structure of finite groups that satisfy the converse to Lagrange’s Theorem
 15.01.2024 Torben Wiedemann (Universität Giessen) Root graded groups
 22.01.2024 Sam Corson (Universidad del País Vasco) Many trivially generated groups are the same
Abstract: Lagrange’s Theorem, which is one of the most important theorems in finite group theory states that the order of a subgroup H of a finite group G divides the order of G. In this project, we investigate the converse to Lagrange’s Theorem which would say, for every divisor d > 0 of the order of G, there is a subgroup H of G with order d. Groups that satisfy this converse property are known as CLT groups. In this project we study the classes of groups that satisfy the converse to Lagrange’s Theorem and we show that they are between the solvable and supersolvable groups. We give some examples that show that the inclusions are proper.
Abstract: Let Φ be a finite root system. A Φgraded group is a group G together with a family of subgroups (U_{α})_{α ∈ Φ} satisfying some purely combinatorial axioms. The main examples of such groups are the Chevalley groups of type Φ, which are defined over commutative rings and which satisfy the wellknown Chevalley commutator formula. We show that if Φ is of rank at least 3, then every Φgraded group is defined over some algebraic structure (e.g. a ring, possibly noncommutative or, in low ranks, even nonassociative) such that a generalised version of the Chevalley commutator formula is satisfied. A new computational method called the blueprint technique is crucial in overcoming certain problems in characteristic 2. This method is inspired by a paper of RonanTits.
Abstract: When the algebraic generators of a group are all trivial then the group is also trivial. However, when the group is combinatorially described using infinite words, the "generators" can be trivial while the group is uncountable. I will give some background and present recent work showing that many natural examples of such groups are isomorphic.