Abstract
The smallest known thick generalized octagon has order (2, 4) and can be constructed from the parabolic subgroups of the Ree group ^2F4(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 29.
Original language | English |
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Pages (from-to) | 369-393 |
Number of pages | 25 |
Journal | Journal of Algebra |
Volume | 421 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Cayley graph
- Generalized polygon
- Groups of order a small power of 2
- Incidence geometry
- Octagon
- Point-line geometry
- Ree group