Finite p-Irregular Subgroups of PGL2(k)

In the late 19th century, Klein inaugurated a program for describing the finite subgroups of PGL 2 ( k ) by treating the case in which the field k is the complex numbers. Gierster and Moore extended Klein’s arguments to deal with finite fields. In the past century, additional contributions to this p...

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Bibliographic Details
Published in:La matematica 2023-06, Vol.2 (2), p.479-522
Main Author: Faber, Xander
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Research Article
Online Access:Get full text
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Summary:In the late 19th century, Klein inaugurated a program for describing the finite subgroups of PGL 2 ( k ) by treating the case in which the field k is the complex numbers. Gierster and Moore extended Klein’s arguments to deal with finite fields. In the past century, additional contributions to this problem were made by Serre, Suzuki, and Beauville, among others. We complete this program by giving a classification of the finite subgroups of PGL 2 ( k ) with order divisible by p , up to conjugation, for an arbitrary field k of positive characteristic  p .
ISSN:2730-9657
DOI:10.1007/s44007-023-00051-4