Galois and PSL
Péter Pál Pálfy (Hungarian Academy of Sciences)
Abstract: In his "testamentary letter" Galois claims (without proof) that $\text{PSL}(2,p)$ does not have a subgroup of index $p$ whenever $p>11$, and gives examples that for $p = 5, 7, 11$ such subgroups exist.
The attempt by Betti in 1853 to give a proof does not seem to be complete. Jordan's proof in his 1870 book uses methods certainly not known to Galois. Nowadays we deduce Galois's result from the complete list of subgroups of $\text{PSL}(2,p)$ obtained by Gierster in 1881.
In the talk I will give a proof that might be close to Galois's own thoughts.
Last October I exchanged a few e-mails on this topic with Peter M. Neumann. So the talk is in some way a commemoration of him.
group theory
Audience: researchers in the topic
GOThIC - Ischia Online Group Theory Conference
Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.
| Organizer: | Andrea Caranti* |
| *contact for this listing |