Abstract

A generalized Baumslag–Solitar group (GBS-group) is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. A group is large if some finite index subgroup maps onto the free group F₂. An explicit description is given for all index n subgroups in non-large GBS groups. Moreover, we give exact formulas for the numbers of subgroups, normal subgroups, and conjugacy classes of subgroups of each finite index in non-large GBS groups.

中文翻译：

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非大型广义 Baumslag-Solitar 群中的有限指数子群

摘要

广义 Baumslag-Solitar 群 ( GBS-group ) 是作用于具有无限循环边和顶点稳定器的树的有限生成群。如果某个有限索引子群映射到自由群F ₂上，则该群是大群。对非大型 GBS 组中的所有索引n子组给出了明确的描述。此外，我们给出了非大GBS群中每个有限指标的子群的子群数、正态子群数和共轭类数的精确公式。