Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/95691
Title: c-Extensions of the F4(2)-building
Authors: Ivanov, A. A.
Pasechnik, Dmitrii V.
Keywords: DRNTU::Science::Mathematics::Discrete mathematics::Theory of computation
Issue Date: 2002
Source: Ivanov, A. A., & Pasechnik, D. V. (2002). c-Extensions of the F4(2)-building. Discrete Mathematics, 264(1-3), 91–110.
Series/Report no.: Discrete mathematics
Abstract: We construct four geometries ε1,..., ε4 with the diagram such that any two elements of type 1 are incident to at most one common element of type 2 and three elements of type 1 are pairwise incident to common elements of type 2 if and only if they are incident to a common element of type 5. The automorphism group Ei of εi is flag-transitive, isomorphic to 2E6(2): 2,3.2 E6(2) :2,226: F4(2) and E6(2) : 2, for i=1,2,3 and 4. We calculate the suborbit diagram of the collinearity graph of εi with respect to the action of Ei. By considering the elements in εi fixed by a subgroup Ti of order 3 in Ei we obtain four geometries T1,...,T4 with the diagram on which CEi(Ti) induces flag-transitive action, isomorphic to U6(2): 2,3. U6(2): 2, 214: Sp6(2) and L6(2): 2 for i=1,2,3 and 4. Next, by considering the elements fixed by a subgroup Si of order 7 in Ei we obtain four geometries with the diagram on which CEi(Si) induces flag-transitive action isomorphic to L3(4): 2, 3.L3(4): 2, 28: L3(2) and (L3(2)xL3(2)): 2, for i=1,2,3 and 4.
URI: https://hdl.handle.net/10356/95691
http://hdl.handle.net/10220/8273
DOI: http://dx.doi.org/10.1016/S0012-365X(02)00554-X
Rights: © 2002 Elsevier Science B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Discrete Mathematics, Elsevier Science B.V. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: DOI [http://dx.doi.org/10.1016/S0012-365X(02)00554-X].
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