COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Quotients of groups by torsion elements

## Quotients of groups by torsion elementsAdd to your list(s) Download to your calendar using vCal - Dr. Maurice Chiodo, The University of Milan
- Friday 23 November 2012, 14:00-15:00
- 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 non-trivial 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 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. We give an explicit construction of a finitely presented group which is not torsion-free, and for which the first quotient by torsion elements is again not torsion-free. 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 torsion-free group. This is a joint work with Rishi Vyas. This talk is part of the Junior Algebra/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Junior Algebra/Logic/Number Theory seminar
- MR4
- School of Physical Sciences
- bld31
- ndb35's list
Note that ex-directory lists are not shown. |
## Other listsCambridge-QMUL Phi Workshop MedSin Cambridge anthropology## Other talksViral infection dynamics in transplant recipients undergoing immunosuppression Saving the People of the Forest: one chocolate bar and one nebulizer treatment at a time Stakeholder perceptions across scales of governance: areas of controversy and consensus related to the Indonesian peatland fires Bears, Bulls and Boers: Market Making and Southern African Mining Finance, 1894-1899 Deep & Heavy: Using machine learning for boosted resonance tagging and beyond |