Automorphism groups of locally compact connected double loops are locally compact
type: Item
instance of: scholarly article
title: Automorphism groups of locally compact connected double loops are locally compact
zbMATH Open document ID: 0783.22001
DOI: 10.1007/BF01198727
author: Richard Bödi
published in: Archiv der Mathematik
publication date: 1993-11-15T00:00:00Z
review text: It is a well known fact that the group \(\Sigma\) of all continuous collineations of a compact projective plane is a locally compact transformation group with respect to the compact-open topology [see \textit{H. Salzmann}, Pac. J. Math. 60, 217-234 (1975; Zbl 0323.50009) or \textit{Th. Grundhöfer}, Geom. Dedicata 21, 291-298 (1986; Zbl 0601.51020)]. This implies that the automorphism group \(\Gamma\) of a locally compact connected ternary field is locally compact, since such a ternary field coordinatizes some compact projective plane. In this paper this is generalized to the double loop case, i.e. it is proved that the automorphism group of a locally compact connected double loop is a locally compact transformation group with respect to the compact-open topology.
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 22D45
Mathematics Subject Classification ID: 51N25
zbMATH DE Number: 446395
zbMATH Keywords: automorphism group
zbMATH Keywords: locally compact connected double loop
zbMATH Keywords: locally compact transformation group
zbMATH Keywords: compact-open topology
MaRDI profile type: Publication
cites work: Automorphism groups of compact projective planes
cites work: Q3972230
cites work: Topologische Loops
cites work: Homogene kompakte projektive Ebenen
full work available at URL: https://doi.org/10.1007/bf01198727
OpenAlex ID: W2085440637
description: scientific article; zbMATH DE number 446395