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Coset diagrams and their application to finitely presented groups

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If you have a question about this talk, please contact Joanna Fawcett.

Graphs were first used explicitly in group theory by A.Cayley in 1878, where the vertices were taken to be the elements from a group. These diagrams have provided a useful tool for proving results about free groups, and in particular the result that any subgroup of a free group is free. The notion of a Cayley diagram was extended by O.Schreier, where vertices are now taken to be cosets for a subgroup. The aim of the talk is to highlight how useful these diagrams can be in the study of finitely presented groups by giving two applications: 1) Providing a “nice” presentation for PSL (2,Z). 2) Proving that some infinite families of finitely presented groups give infinite groups.

This talk is part of the Junior Algebra and Number Theory seminar series.

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