This article is cited in 5 papers

On the root-class residuality of certain HNN-extensions of groups

E. A. Tumanova

Ivanovo State University, 39 Ermak str., Ivanovo, 153025 Russia

Abstract: 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.

UDC: 512.543

Received: 13.01.2020
Revised: 28.04.2020
Accepted: 29.06.2020

DOI: 10.26907/0021-3446-2020-12-41-50

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:12, 38–45

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