A Necessary Condition for The Residual Nilpotence of HNN-Extensions
Evgeny Viktorovich Sokolov · Lobachevskii Journal of Mathematics · 2018
Let G be amultiple HNN-extension of a group A , and let all its associated subgroups be properly contained in some locally nilpotent subgroup of A . We prove that if G is residually nilpotent, then all the associated subgroups are p ′-isolated in A for some prime p . Moreover, if q is a prime such that G is residually a q ′-torsion-free nilpotent group, then p = q .