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Generalized towers of flag-transitive circular extensions of a non- classical \(C_ 3\)-geometry. (English) Zbl 0805.51006
The authors’ abstract: “The classification of generalized towers of flag-transitive circular extensions of the sporadic \(A_ 7\)-geometry is completed by characterizing two flat geometries on 16 points, constructed in terms of the Steiner system \(S(24,8,5)\), as the flag-transitive circular extensions of the duals of the sporadic \(A_ 7\)-geometry and the Neumaier geometry for \(A_ 8\), and then by showing the non-existence of flag-transitive circular extensions of these geometries”.

MSC:
51E24 Buildings and the geometry of diagrams
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[1] Conway, J.H, Atlas of finite groups, (1985), Clarendon Oxford
[2] Buekenhout, F; Hubaut, X, Locally polar spaces and related rank 3 groups, J. algebra, 45, 391-434, (1977) · Zbl 0351.05021
[3] Buekenhout, F, The basic diagram of a geometry, (), 1-29
[4] Del Fra, A; Ghinelli, D; Meixner, T; Pasini, A, Flag-transitive extensions of Cn geometries, Geom. dedicata, 37, 253-273, (1991) · Zbl 0722.51007
[5] Meixner, T, Some polar towers, European J. combin., 12, 397-415, (1991) · Zbl 0753.05016
[6] Lunardon, G; Pasini, A, Finite Cn geometries: A survey, Note mat., 5, (1990) · Zbl 0753.51008
[7] Neumaier, A, Some sporadic geometries related to PG(3, 2), Arch. math., 42, 89-96, (1984) · Zbl 0509.05026
[8] Pasini, A; Yoshiara, S, Flag-transitive buekenhout geometries, (), 403-448 · Zbl 0774.51003
[9] Weiss, R; Yoshiara, S, A geometric characterization of the groups suz and HS, J. algebra, 133, 182-196, (1990) · Zbl 0704.20015
[10] Yoshiara, S, On some extended dual polar spaces I, European J. combin., 15, 73-86, (1994) · Zbl 0792.51009
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