Non-congruence presentations of finite simple groups
Group Theory
2024-07-30 v1 Algebraic Geometry
Number Theory
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 in [CLT24]), and that if has a non-trivial Schur multiplier, then it admits a smooth cover (as conjectured in [CFLZ]).
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Cite
@article{arxiv.2407.19047,
title = {Non-congruence presentations of finite simple groups},
author = {William Y. Chen and Alexander Lubotzky and Pham Huu Tiep},
journal= {arXiv preprint arXiv:2407.19047},
year = {2024}
}
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29 pages