On the root-class residuality of certain HNN-extensions of groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 41-50
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Let $\mathcal{K}$ be a root class of groups and $G$ be an HNN-extension of a group $B$ with subgroups $H$ and $K$ associated by an isomorphism $\varphi\colon H \to K$. We obtain certain sufficient conditions for $G$ to be residually a $\mathcal{K}$‑group provided the set $\{h^{-1}(h\varphi) \mid h \in H\}$ is a normal subgroup of $B$ or there exists an automorphism $\alpha$ of $B$ such that $H\alpha = K$. In particular, we find sufficient conditions for $G$ to be residually solvable, residually periodic solvable, or residually finite solvable in the case when $B$ is residually nilpotent while $H$ and $K$ are cyclic and map onto each other by an automorphism of $B$.
Keywords:
HNN-extension, root-class residuality, residual finiteness, residual $p$-finiteness, residual solvability.
@article{IVM_2020_12_a4,
author = {E. A. Tumanova},
title = {On the root-class residuality of certain {HNN-extensions} of groups},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {41--50},
publisher = {mathdoc},
number = {12},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2020_12_a4/}
}
E. A. Tumanova. On the root-class residuality of certain HNN-extensions of groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 41-50. http://geodesic.mathdoc.fr/item/IVM_2020_12_a4/