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SUMMARY:Quotients of groups by torsion elements - Dr. Maurice Chiodo\, The
  University of Milan
DTSTART:20121123T140000Z
DTEND:20121123T150000Z
UID:TALK41242@talks.cam.ac.uk
CONTACT:Joanna Fawcett
DESCRIPTION:It is well known that if we take a group G\, and quotient out 
 by the normal closure of all non-trivial commutators\, then the resulting 
 group is abelian (and in some sense “universal”). However\, if we inst
 ead quotient out by the normal closure of all torsion elements of G\, then
  the resulting group need not be torsion-free. But\, by taking a countably
  infinite “tower” of quotients of torsion elements\, we do eventually 
 come to a torsion-free group\, which is universal in the same way that the
  abelianisation is.\nWe give an explicit construction of a finitely presen
 ted group which is not torsion-free\, and for which the first quotient by 
 torsion elements is again not torsion-free. We extend this construction\,\
 nand combine it with some classical embedding results\, to construct a fin
 itely generated (and recursively presented) group for which no finite iter
 ation of quotients by torsion elements yields a\ntorsion-free group. This 
 is a joint work with Rishi Vyas.
LOCATION:MR4
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