Quotients of groups by torsion elements
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 Dr. Maurice Chiodo, The University of Milan
 Friday 23 November 2012, 14:0015:00
 MR4.
If you have a question about this talk, please contact Joanna Fawcett.
It is well known that if we take a group G, and quotient out by the normal closure of all nontrivial commutators, then the resulting group is abelian (and in some sense “universal”). However, if we instead quotient out by the normal closure of all torsion elements of G, then the resulting group need not be torsionfree. But, by taking a countably infinite “tower” of quotients of torsion elements, we do eventually come to a torsionfree group, which is universal in the same way that the abelianisation is.
We give an explicit construction of a finitely presented group which is not torsionfree, and for which the first quotient by torsion elements is again not torsionfree. We extend this construction,
and combine it with some classical embedding results, to construct a finitely generated (and recursively presented) group for which no finite iteration of quotients by torsion elements yields a
torsionfree group. This is a joint work with Rishi Vyas.
This talk is part of the Junior Algebra and Number Theory seminar series.
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