# Algebra seminar in Lincoln: talk by Professor Brita Nucinkis

On Wednesday the 15th of November, Professor Brita Nucinkis (Royal Holloway, University of London) visited School of Mathematics and Physics in Lincoln. She gave a talk “*Centralisers in generalised Thompson groups*” at the Lincoln Algebra Seminar.

*Abstract*: We define a family of groups that generalises Thompson’s group , and also its generalisations by Higman, Stein and Brin. These groups are defined as automorphism groups of certain Cantor-algebras. We give a description of centralisers of finite subgroups and show, that, under some mild hypotheses on the Cantor-algebra, they are of type . Centralisers of infinite order elements, on the other hand, are far less well-understood; they have been described for Higman’s groups by Bleak et al., but even for Brin’s group we only have partial results. In this talk I give a survey of the construction and of the results for centralisers of finite subgroups, and give some indication on the sort of results one can get for centralisers of infinite order elements in . This is joint work with Belk, Martinez-Perez, and Matucci.

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