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University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Some different types of Universal finitely presented groups.

## Some different types of Universal finitely presented groups.Add to your list(s) Download to your calendar using vCal - 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/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
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