Non-congruence presentations of finite simple groups

William Y. Chen; Alexander Lubotzky; Pham Huu Tiep

doi:10.4171/rlm/1078

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Non-congruence presentations of finite simple groups

William Y. Chen
University of Illinois at Urbana-Champaign, USA
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Alexander Lubotzky
The Weizmann Institute of Science, Rehovot, Israel
Pham Huu Tiep
Rutgers University, Piscataway, USA

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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 $S$ 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)).

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. (2026), published online first

DOI 10.4171/RLM/1078