Eine Bemerkung über die Gruppen PGL(2,F). (A remark on the groups PGL(2,F))
type: Item
instance of: scholarly article
title: Eine Bemerkung über die Gruppen PGL(2,F). (A remark on the groups PGL(2,F))
zbMATH Open document ID: 0694.20003
DOI: 10.1007/BF03322618
author: W. Kerby
published in: Results in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author proves the following theorem: A KT-field \((F,+,\cdot,\sigma)\) is a commutative field iff the set \(R:=\{x\sigma (x^{-1})|\) \(x\in F^*\}\) is contained in the center of \((F^*,\cdot)\). Because of the unique connection between KT-fields and sharply 3-transitive groups one also gets an analogous characterisation of PGL(2,F).
Mathematics Subject Classification ID: 20B22
Mathematics Subject Classification ID: 12K05
zbMATH DE Number: 4136199
zbMATH Keywords: PGL(2,K)
zbMATH Keywords: commutative field
zbMATH Keywords: KT-fields
zbMATH Keywords: sharply 3-transitive groups
reviewed by: Heinrich Wefelscheid
MaRDI profile type: Publication
cites work: Q5187377
cites work: Q4041787
cites work: A structure theorem for KT-nearfields
cites work: Über eine scharf 3-fach transitiven Gruppen zugeordnete algebraische Struktur
cites work: Fastkoerper mit multiplikativer FC-Gruppe
cites work: Lokalkompakte Fastkörper. (Locally compact nearfields)
full work available at URL: https://doi.org/10.1007/bf03322618
OpenAlex ID: W2137815419
description: scientific article; zbMATH DE number 4136199