2015/10/27 by Anurag Bishnoi, Bishnoi, Anurag, Bart De Bruyn +1
Mathematics · #05E18 #51E12 #51E25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:05E18 #msc:51E12 #msc:51E25
paper · pdf · doi:10.48550/arxiv.1510.07919
20 pages; some revisions based on referee reports; added more references; added remarks 1.4 and 1.5; corrected typos; improved the overall exposition
arxiv created 2016/05/13 · arxiv updated 2016/05/16
In recent work, we constructed a new near octagon G from certain involutions of the finite simple group G2(4) and showed a correspondence between the Suzuki tower of finite simple groups, L3(2) < U3(3) < J2 < G2(4) < Suz, and the tower of near polygons, H(2,1) ⊂ H(2)D ⊂ HJ ⊂ G. Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall-Janko near octagon HJ is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters (2, 4; 0, 3), but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, H(2)D. We also give a complete classification of near hexagons of order (2, 2) and use it to prove the uniqueness result for H(2)D.