Lack of profinite rigidity among extensions with free quotient
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- by Paweł Piwek;
- Trans. Amer. Math. Soc. 378 (2025), 635-650
- DOI: https://doi.org/10.1090/tran/9268
- Published electronically: September 25, 2024
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Abstract:
We present a construction that yields infinite families of non-isomorphic semidirect products $N \rtimes F_m$ sharing a specified profinite completion. Within each family, $m \ge 2$ is constant and $N$ is a fixed group. For $m=2$ we can take $N$ to be free of rank $\ge 10$, free abelian of rank $\ge 12$, or a surface group of genus $\ge 5$.References
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Bibliographic Information
- Paweł Piwek
- Affiliation: Radcliffe Observatory, University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United Kingdom
- ORCID: 0000-0003-4766-3947
- Email: pawel.piwek@maths.ox.ac.uk
- Received by editor(s): March 5, 2024
- Received by editor(s) in revised form: June 11, 2024, and June 24, 2024
- Published electronically: September 25, 2024
- Additional Notes: This work was supported by the Mathematical Institute Scholarship of University of Oxford.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 635-650
- MSC (2020): Primary 20E26; Secondary 20E18
- DOI: https://doi.org/10.1090/tran/9268
- MathSciNet review: 4840317