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Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 281–285 | Cite as

A Necessary Condition for The Residual Nilpotence of HNN-Extensions

  • E. V. Sokolov
Article
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Abstract

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.

Keywords and phrases

multiple HNN-extension residual nilpotence residual p-finiteness 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Ivanovo State UniversityIvanovoRussia

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