Charlotte Scott Centre for Algebra

On Wednesday 24 January, **Dr Maurice Chiodo (University of Cambridge)** visited Lincoln and gave a talk “*Quotients of groups by torsion elements*”.

*Abstract*: The quotient of a group $latex G$ by the normal closure $latex N$ of all its torsion elements need not be torsion-free. However, iterating this process a countably-infinite number of times yields the universal torsion-free quotient of $latex G$. With this in mind, we define the Torsion Length of a group to be the minimum number of such quotients needed to yield a torsion-free group (or $latex omega$ if no such number exists). Finding examples of groups with infinite torsion length is somewhat tricky, especially if one restricts to finitely presented, or even finitely generated groups. I’ll aim to discuss some of these examples, and give an overview of how the constructions work.

This is a joint work with Rishi Vyas.

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