Finite index subgroups in non-large generalized Baumslag–Solitar groups

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.

Keywords:

• Baumslag–Solitar group
• finite index subgroup
• generalized Baumslag–Solitar group
• non-large group

2020 Mathematics Subject Classification::

• 20E06
• 20E07
• 20E08

Additional information

Funding

The work was supported by Russian Science Foundation (project 19-11-00039).