Finite-presentability conjecture for generalised Wilson groups

A generalised Wilson group is an infinitely iterated wreath product of finite non-abelian simple permutation groups of the type considered in the paper. A profinite group is finitely presentable if it admits a presentation with finitely many generators and finitely many defining relations in the profinite category. Finite-presentability conjecture. Every generalised Wilson group is not finitely presentable. The paper proves non-finite-presentability for broad families, including infinitely iterated wreath products built from a sequence in which a fixed prime divides the relevant Schur multipliers infinitely often, but does not prove the statement for all generalised Wilson groups.