355 KB33 KB200820252017Green, R. M.Saniga, Metodletnik:12številka:2str. 287-299COBISSID:18164825ISSN:1855-3966URN:URN:NBN:SI:doc-KBTTA1VLenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneabližnji heksagonigeometrijske hiperravnineVeldkampovi prostoriA classification of the Veldkamp lines of the near hexagon Lsub3timesGQ(2, 2)|Using a standard technique sometimes (inaccurately) known as Burnside's Lemma, it is shown that the Veldkamp space of the near hexagon ?$L_3 \times \text{GQ}(2, 2)$? features 156 different types of lines. We also give an explicit description of each type of a line by listing the types of the three geometric hyperplanes it consists of and describing the properties of its core set, that is the subset of points of ?$L_3 \times \text{GQ}(2, 2)$? shared by the three geometric hyperplanes in questionZ uporabo standardne tehnike, včasih (netočno) poimenovane Burnsideova lema, pokažemo, da ima Veldkampov prostor bližnjega šestkotnika ?$L_3 \times \text{GQ}(2, 2)$? 156 različ- nih vrst premic. Podamo tudi ekspliciten opis vsakega tipa premic na ta način, da podamo seznam tipov treh geometrijskih hiperravnin, iz katerih sestoji, in opišemo lastnosti njegove jedrne množice, to je podmnožice točk prostora ?$L_3 \times \text{GQ}(2, 2)$?, skupnih ustreznim trem geometrijskim hiperravninamTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije