A Necessary Condition for The Residual Nilpotence of HNN-Extensions
- Autores: Sokolov E.1
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Afiliações:
- Ivanovo State University
- Edição: Volume 39, Nº 2 (2018)
- Páginas: 281-285
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201684
- DOI: https://doi.org/10.1134/S1995080218020257
- ID: 201684
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Resumo
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.
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Sobre autores
E. Sokolov
Ivanovo State University
Autor responsável pela correspondência
Email: ev-sokolov@yandex.ru
Rússia, Ivanovo, 153025