Fachbereich
Mathematik und Statistik

Universität
Konstanz

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Block Seminar on Jordan groups

This is the homepage of the Block Seminar on Jordan groups, which will take place from the 27th of February until the 3rd of March.

Organisers

Prof. Dr. Salma Kuhlmann and Gabriel Lehéricy

Speaker

David Bradley-Williams

Schedule

All talks will take place in F426 from 13:30 to 15:00, according to the table below.

DateTopic
Monday27.02Background on permutation groups
Tuesday28.02Relations related to betweenness
Wednesday01.03 Structure theorems for primitive Jordan groups
Thursday02.03Variants of o-minimality
Friday03.03Applications of the theory of Jordan groups

Contents

In these lectures we will be considering structural theorems for a class of infinite permutation groups called Jordan groups, viewing them as automorphism groups of infinite first-order structures. They may arise as automorphism group of semilinearly ordered trees and study of Jordan groups leads towards relational structures arising from such trees: betweeness relations, C-relations and D-relations. We will discuss what these are and how they are interrelated. We will discuss theorems that tell us what structures appear as invariant structures for a Jordan group and some ways those theorems have recently been applied in identifying some families of maximally closed subgroups of Sym(N).

Prerequisites

Graduate-level algebra and some model theory.

References

  • S. A. Adeleke and D. Macpherson, Classification of infinite primitive Jordan permutation groups, Proc. London Math. Soc. (3) 72 (1996) 63 -- 123.
  • S. A. Adeleke and P. M. Neumann, Relations Related to Betweenness: Their Structure and Automorphisms, Mem. Amer. Math. Soc. 623 (1998).
  • S. A. Adeleke and P. M. Neumann, Primitive permutation groups with primitive Jordan sets, J. London Math. Soc. (2) 53 (1996) 209--229.
  • Further references on specific topics might be given in due time
  • M. Bhattacharjee, D. Macpherson, R. G. Möller and P. M. Neumann, Notes on Infinite Permutation Groups, Lecture Notes in Math., Springer 1698 (1998) and Hindustan Book Agency (1997).
  • P. Cameron, Oligomorphic permutation groups, London Mathematical Society Lecture Note Series, 152, Cambridge University Press, Cambridge (1990).
  • M. Droste, Structure of partially ordered sets with transitive automorphism groups, Mem. Amer. Math. Soc. 334 (1985).

    • Target group: MA, PhD's and Post-Docs.
    Language: English