PreprintCC BY 4.0arXiv
Galois's lost proof on PSL(2,p)
Abstract
In his famous ``testamentary letter'' Galois formulated several results without proof. Among them he claimed --- here we express it in modern terms --- that the projective special linear group PSL(2,p) has a subgroup of index p only for p≤ 11. Nowadays this result is seen as a corollary of the complete enumeration of all subgroups of PSL(2,p) obtained by Gierster in 1881. In this paper we attempt to give a proof that uses only methods available to Galois.
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BibTeX
@misc{palfy2026galoiss,
title = {{Galois's lost proof on $PSL(2,p)$}},
author = {Péter P. Pálfy},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06054},
eprint = {2611.06054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06054},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Galois's lost proof on PSL(2,p)
AU - Péter P. Pálfy
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06054
UR - https://arxiv.org/abs/2611.06054
AB - In his famous ``testamentary letter'' Galois formulated several results without proof. Among them he claimed --- here we express it in modern terms --- that the projective special linear group PSL(2,p) has a subgroup of index p only for p≤ 11. Nowadays this result is seen as a corollary of the complete enumeration of all subgroups of PSL(2,p) obtained by Gierster in 1881. In this paper we attempt to give a proof that uses only methods available to Galois.
ER -