Certain residual properties of HNN-extensions with central associated subgroups

2021/06/25 by E. V. Sokolov, Sokolov, E. V. · 1 citation
Mathematics · #20E06 #20E26 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20E06 #msc:20E26

paper · pdf · doi:10.48550/arxiv.2106.13866

25 pages; the English version of the previously published Russian original

openalex publication_date 2021/06/25 · arxiv created 2021/06/29 · arxiv updated 2021/06/30 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28

Abstract

Suppose that G is a group, H and K are proper isomorphic central subgroups of G, and \mathfrakG is an HNN-extension of G with the associated subgroups H and K. We prove necessary and sufficient conditions for \mathfrakG to be residually a C-group, where C is a class of groups closed under taking subgroups, extensions, homomorphic images, and Cartesian products of the form ∏_{y ∈ Y}X_y, where X, Y ∈ C and X_y is an isomorphic copy of X for each y ∈ Y.

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• Certain residual properties of HNN-extensions with normal associated subgroups

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