Abstract

How difficult is it to compute if a group contains inversions? What are obstructions to computing invariants related to torsion in groups? What can we say about groups with infinite `torsion length’ (the minimum number of times one needs to `kill the torsion’ in a group to get a torsion-free group)? What sort of torsion properties are preserved by standard embedding theorems?

I’ll discuss some recent results relating to these. In particular, I’ll explain how the Higman Embedding Theorem preserves both torsion length and the set of torsion orders, how we can construct a finitely presented C’(1/6) group with infinite torsion length, how we can kill off subsets of torsion orders in groups, and how we can get `universal’ finitely presented groups which exclude certain sets of torsion orders.