, Volume 85, Issue 1-3, pp 11-18

Some remarks on profinite HNN extensions

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We extend a construction of Higman, Neumann and Neumann [LS, IV.3.1] and show that every profinite groupG with only countably many open subgroups embeds in a 2-generated profinite groupE in which all torsion elements are conjugate to elements ofG; ifG is pro-p,E can be chosen pro-p. This answers a question of Wilson (oral communication) and generalises a result of Lubotzky and Wilson [LW].