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Bibliographic Details
Main Authors:	Shen, Hanwen, Ushakov, Alexander
Format:	Preprint
Published:	2025
Subjects:	Group Theory Computational Complexity Combinatorics
Online Access:	https://arxiv.org/abs/2510.03801
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Table of Contents:

Let $G=F\ast_φt$ be an HNN extension of a free group $F$ with two equal associated normal subgroups $H_1 = H_2$ of finite index. We prove that the word problem in $G$ is decidable in polynomial time. This result extends to the case where the subgroups $H_1=H_2$ are not normal, provided that the isomorphism $φ:H_1\to H_2$ satisfies an additional condition described in Section 5.