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.
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Button, J.O. Strictly ascending HNN extensions in soluble groups. Ricerche mat. 61, 139–145 (2012). https://doi.org/10.1007/s11587-011-0120-2
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DOI: https://doi.org/10.1007/s11587-011-0120-2