Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons

Inspired by a theorem Skornjakov-Hughes-Pasini [9, 7, 8] and problem which turned up in our recent paper [13], we start study of epimorphisms with source thick generalized m-gon target thin m-gon. In this first part the series, classify cases m = 3, 4 6 when polygons are finite. Then show that infinite case is very different, construct examples strongly deviate from finite case. A number general structure theorems also obtained. We introduce theory locally finitely generated chained along way.