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Epimorphisms of generalized polygons, B: The octagons

Joseph A. Thas and Koen Thas

Vol. 20 (2023), No. 2-3, 579–597
Abstract

This is the second part of our study of epimorphisms with source a thick generalized m-gon and target a thin generalized m-gon. We classify the case m = 8 when the polygons are finite (in the first part (2022) we handled the cases m = 3,4 and 6). Then we show that the infinite case is very different, and construct examples which strongly differ from the finite case. A number of general structure theorems are obtained, and we also take a look at the infinite case for general gonality.

Keywords
generalized polygon, generalized octagon, epimorphism, thin octagon
Mathematical Subject Classification
Primary: 20B25, 20B27, 51B25, 51E12
Milestones
Received: 25 October 2022
Revised: 28 April 2023
Accepted: 4 July 2023
Published: 13 September 2023
Authors
Joseph A. Thas
Department of Mathematics: Algebra and Geometry
Ghent University
Ghent
Belgium
Koen Thas
Department of Mathematics: Algebra and Geometry
Ghent University
Ghent
Belgium