Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons
Combinatorics
2022-08-17 v1
Abstract
Inspired by a theorem by Skornjakov-Hughes-Pasini [9, 7, 8] and a problem which turned up in our recent paper [13], we start a study of epimorphisms with source a thick generalized m-gon and target a thin generalized m-gon. In this first part of the series, we classify the cases m = 3, 4 and 6 when the polygons are finite. Then we show that the infinite case is very different, and construct examples which strongly deviate from the finite case. A number of general structure theorems are also obtained. We introduce the theory of locally finitely generated generalized polygons and locally finitely chained generalized polygons along the way.
Keywords
Cite
@article{arxiv.2201.03901,
title = {Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons},
author = {Joseph A. Thas and Koen Thas},
journal= {arXiv preprint arXiv:2201.03901},
year = {2022}
}
Comments
16 pages; submitted (August 2021)