On the sharply 1-transitive subsets of \(PGL(2,p^ m)\)
type: Item
instance of: scholarly article
title: On the sharply 1-transitive subsets of \(PGL(2,p^ m)\)
zbMATH Open document ID: 0639.51010
DOI: 10.1007/BF01222383
published in: Journal of Geometry
publication date: 1988-01-01T00:00:00Z
review text: The main aim of the author's investigation is to prove a proposition which can be considered as one further step towards the verification of the following conjecture: If p is odd then every sharply 1-transitive subset R of \(PGL(2,p^ m)\) such that id\(\in R\) is necessarily a subgroup. The author enumerates some low values of \(p^ m\) for which the conjecture was verified to be true, and then he proves the following main result: If p is odd and R is a sharply 1-transitive subset of \(PGL(2,p^ m)\) such that id\(\in R\), then either \(<R>=R\) or \(<R>=PSL(2,p^ m)\) or \(<R>=PGL(2,p^ m)\).
reviewed by: J.Libicher
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 4042691
zbMATH Keywords: sharply 1-transitive subsets of \(PGL(2,p^ m)\)
author: A. Bonisoli
MaRDI profile type: Publication
cites work: Q5674022
cites work: Q3797366
cites work: Q3694152
cites work: A combinatorial characterization of the dihedral subgroups of order \(2(p^r+1)\) of \(PGL(2,p^r)\)
cites work: Q4131245
description: scientific article; zbMATH DE number 4042691