Margulis-Soifer theorem for one-relator groups

@misc{akhmedov2026margulissoifer,
  title = {{Margulis-Soifer theorem for one-relator groups}},
  author = {Azer Akhmedov and Atabay Mahmudov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25125},
  eprint = {2609.25125},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25125},
}

TY  - UNPB
TI  - Margulis-Soifer theorem for one-relator groups
AU  - Azer Akhmedov
AU  - Atabay Mahmudov
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.25125
UR  - https://arxiv.org/abs/2609.25125
AB  - We establish the Margulis-Soifer dichotomy for one-relator groups: every one-relator group is either virtually solvable or has a maximal subgroup of infinite index. We also present examples of one-relator groups with and without free maximal subgroups of infinite index, as well as examples that possess both free and non-free infinite index maximal subgroups. Triviality of the Frattini subgroup is also shown for all non-solvable one-relator groups. We close the paper with a short list of questions.
ER  -