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On the Root-Class Residuality of Certain HNN-Extensions of Groups

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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.

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Funding

This work was funded by Russian Foundation for Basic Research, project no. 18-31-00187.

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Authors and Affiliations

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

    E. A. Tumanova

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  1. E. A. Tumanova
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Correspondence to E. A. Tumanova.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 41–50.

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Tumanova, E.A. On the Root-Class Residuality of Certain HNN-Extensions of Groups. Russ Math. 64, 38–45 (2020). https://doi.org/10.3103/S1066369X20120051

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