Abstract
We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple group S admits a non-congruence presentation (as conjectured by Chen, Lubotzky, and Tiep (2024)), and that if S has a non-trivial Schur multiplier, then it admits a smooth cover (as conjectured by Chen, Fan, Li, and Zhu (2024)).
| Original language | English |
|---|---|
| Pages (from-to) | 445-483 |
| Number of pages | 39 |
| Journal | Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova |
| Volume | 36 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2025 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:©2026 Accademia Nazionale dei Lincei Published by EMS Press. This work licensed under a CC BY 4.0 license, Licensed under the Creative Commons Attribution 4.0 International License CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
Keywords
- congruence subgroups
- finite simple groups
- generators
- presentations
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