标题： 关于循环JSJ分解的同构问题：顶点消去 显示英文标题

标题： On the isomorphism problem for cyclic JSJ decompositions: vertex elimination

摘要： 我们介绍了图上的群的两个新操作，这些操作具有循环边群，并保留基本群。 这些操作使我们能够在不使用扩展的情况下解决同构问题，因此在见证两个群之间同构的移动序列中，保持顶点和边的数量不变。 我们进一步表明，一个大型循环JSJ分解族的同构问题可以简化为广义Baumslag-Solitar群（GBS）的情况，并且在GBS中，只需考虑单顶点图即可。 作为方法的应用，我们解决了柔性GBS的一个广泛类别的同构问题。 最后，我们讨论了我们技术的潜在进一步应用。 显示英文摘要

摘要： We introduce two new moves on graphs of groups with cyclic edge groups that preserve the fundamental group. These moves allow us to address the isomorphism problem without the use of expansions, therefore keeping the number of vertices and edges constant along sequences of moves witnessing an isomorphism between two groups. We further show that the isomorphism problem for a large family of cyclic JSJ decompositions reduces to the case of generalized Baumslag-Solitar groups (GBS), and that among GBSs, it suffices to consider one-vertex graphs. As an application of the methods, we solve the isomorphism problem for a broad class of flexible GBSs. Finally, we discuss potential further applications of our techniques.