Certain residual properties of HNN-extensions with normal associated subgroups

2025/05/01 by E. V. Sokolov, Sokolov, E. V., E. A. Tumanova +1
Engineering · Mathematics · #20E26 (Primary) 20E06 (Secondary) #Elasticity and Wave Propagation #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.00262

openalex publication_date 2025/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 𝔼 be the HNN-extension of a group B with subgroups H and K associated according to an isomorphism φ\colon H → K. Suppose that H and K are normal in B and (H ∩ K)φ= H ∩ K. Under these assumptions, we prove necessary and sufficient conditions for 𝔼 to be residually a C-group, where C is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual p-finiteness of the group 𝔼.

Citations

• On conditions for the approximability of the fundamental groups of graphs of groups by root classes of groups
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• Certain residual properties of HNN-extensions with central associated subgroups
• A characterization of root classes of groups
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Related

• Certain residual properties of HNN-extensions with central associated subgroups
• A criterion for HNN extensions of finite p-groups to be residually p
• On the Residuality a Finite Group of HNN-Extensions
• HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem
• On the linearity of HNN-extensions with abelian base group