Some different types of Universal finitely presented groups.

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• Maurice Chiodo (The University of Melbourne)
• Friday 25 February 2011, 14:00-15:00
• MR4.

If you have a question about this talk, please contact Chris Bowman.

For P an algebraic property of groups, we call a finitely presented group G “Universally-P” if both of the following occur: 1. G has property P. 2. Every finitely presented group H with property P embeds in G. Using the Higman embedding theorem, it has been shown that there exists a Universally-everything group; a finitely presented group in which every finitely presented group embeds. We will use some straightforward arguments to show that Universally-abelian groups do not exist (nor do Universally-nilpotent or Universally-soluble groups), yet universally-free groups do. Then, by closely analysing the Higman embedding theorem we will show that there exists a Universally-(torsion free) group.

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

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