JournalsrlmVol. 36, No. 3pp. 445–483

Non-congruence presentations of finite simple groups

  • William Y. Chen

    University of Illinois at Urbana-Champaign, USA

  • Alexander Lubotzky

    The Weizmann Institute of Science, Rehovot, Israel

  • Pham Huu Tiep

    Rutgers University, Piscataway, USA
Non-congruence presentations of finite simple groups cover
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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 admits a non-congruence presentation (as conjectured by Chen, Lubotzky, and Tiep (2024)), and that if has a non-trivial Schur multiplier, then it admits a smooth cover (as conjectured by Chen, Fan, Li, and Zhu (2024)).

Cite this article

William Y. Chen, Alexander Lubotzky, Pham Huu Tiep, Non-congruence presentations of finite simple groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 36 (2025), no. 3, pp. 445–483

DOI 10.4171/RLM/1078