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SUMMARY:Some different types of Universal finitely presented groups. - Mau
 rice Chiodo (The University of Melbourne)
DTSTART:20110225T140000Z
DTEND:20110225T150000Z
UID:TALK29944@talks.cam.ac.uk
CONTACT:Chris Bowman
DESCRIPTION:For P an algebraic property of groups\, we call a finitely pre
 sented\ngroup G "Universally-P" if both of the following occur:\n1. G has 
 property P.\n2. Every finitely presented group H with property P embeds in
  G.\nUsing the Higman embedding theorem\, it has been shown that there\nex
 ists a Universally-everything group\; a finitely presented group in\nwhich
  every finitely presented group embeds. We will use some\nstraightforward 
 arguments to show that Universally-abelian groups do\nnot exist (nor do Un
 iversally-nilpotent or Universally-soluble\ngroups)\, yet universally-free
  groups do. Then\, by closely analysing\nthe Higman embedding theorem we w
 ill show that there exists a\nUniversally-(torsion free) group.
LOCATION:MR4
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