PreprintCC BY 4.0arXiv
Polycyclic groups and profinite isomorphism
Abstract
The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem for the class of virtually polycyclic groups.
Related
- An algebro-geometric approach to profinite iterated monodromy groups
- Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infinite Index
- Profinite groups whose closed subgroups are subnormal of defect at most two
- On the measure of definable sets in profinite groups
- Large profinite genus and extensions in Bestvina-Brady groups
BibTeX
@misc{segal2026polycyclic,
title = {{Polycyclic groups and profinite isomorphism}},
author = {Dan Segal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28310},
eprint = {2605.28310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28310},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polycyclic groups and profinite isomorphism
AU - Dan Segal
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2605.28310
UR - https://arxiv.org/abs/2605.28310
AB - The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem for the class of virtually polycyclic groups.
ER -