On the uniqueness of the generalized octagon of order (2,4)

JOURNAL OF ALGEBRA

卷:421

Article

Cohen, Arjeh M.¹  O'Brien, E. A.²  Shpectorov, Sergey³ 

[1] Tech Univ Eindhoven, Dept Math & Comp Sci, Eindhoven, Netherlands

[2] Univ Auckland, Dept Math, Auckland, New Zealand

[3] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

关键词: Generalized polygon;    Octagon;    Point-line geometry;    Incidence geometry;    Groups of order a small power of 2;    Ree group;    Cayley graph;   

DOI  :  10.1016/j.jalgebra.2014.08.034

来源: Elsevier

【 摘 要 】

The smallest known thick generalized octagon has order (2,4) and can be constructed from the parabolic subgroups of the Ree group F-2(4)(2). It is not known whether this generalized octagon is unique up to isomorphism. We show that it is unique up to isomorphism among those having a point a whose stabilizer in the automorphism group both fixes setwise every line on a and contains a subgroup that is regular on the set of 1024 points at maximal distance to a. Our proof uses extensively the classification of the groups of order dividing 2(9). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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