Geodesic
On the Isomorphism of Some Groups with One Defining Relation
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 34-44

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Each of the groups in the class under consideration in the paper is presented by one defining relation depending on three integral parameters and is an HNN-extension of some Baumslag–Solitar group. Necessary and sufficient conditions for two groups of this class to be isomorphic and also for two nonisomorphic groups to be homomorphic images of each other are obtained. A consequence of this fact is the negative answer to Question 3.33 in “The Kourovka Notebook.” 
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A. V. Borshchev; D. I. Moldavanskii. On the Isomorphism of Some Groups with One Defining Relation. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 34-44. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a2/