English

Strictly ascending HNN extensions in soluble groups

Group Theory 2010-04-02 v1

Abstract

We show that there exist finitely generated soluble groups which are not LERF but which do not contain strictly ascending HNN extensions of a cyclic group. This solves Problem 16.2 in the Kourovka notebook. We further show that there is a finitely presented soluble group which is not LERF but which does not contain a strictly ascending HNN extension of a polycyclic group.

Cite

@article{arxiv.1004.0197,
  title  = {Strictly ascending HNN extensions in soluble groups},
  author = {J. O. Button},
  journal= {arXiv preprint arXiv:1004.0197},
  year   = {2010}
}

Comments

10 pages

R2 v1 2026-06-21T15:05:38.046Z