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SUMMARY:Péter Pál Pálfy (Hungarian Academy of Sciences)
DTSTART:20210527T150000Z
DTEND:20210527T160000Z
DTSTAMP:20260423T053141Z
UID:GOThIC/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/29/">
 Galois and PSL</a>\nby Péter Pál Pálfy (Hungarian Academy of Sciences) 
 as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nI
 n his "testamentary letter" Galois claims\n(without proof) that $\\text{PS
 L}(2\,p)$ does not have a subgroup of index $p$\nwhenever $p>11$\, and giv
 es examples that for $p = 5\, 7\, 11$ such subgroups\nexist. \n\nThe attem
 pt by Betti in 1853 to give a proof does not seem to be\ncomplete. Jordan'
 s proof in his 1870 book uses methods certainly not\nknown to Galois. Nowa
 days we deduce Galois's result from the complete\nlist of subgroups of $\\
 text{PSL}(2\,p)$ obtained by Gierster in 1881.\n\nIn the talk I will give 
 a proof that might be close to Galois's own\nthoughts. \n\nLast October I 
 exchanged a few e-mails on this topic with\nPeter M. Neumann. So the talk 
 is in some way a commemoration of him.\n
LOCATION:https://researchseminars.org/talk/GOThIC/29/
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