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The flag-transitive tilde and Petersen-type geometries are all known


Authors: A. A. Ivanov and S. V. Shpectorov
Journal: Bull. Amer. Math. Soc. 31 (1994), 173-184
MSC: Primary 51E24; Secondary 20D08, 20E42
DOI: https://doi.org/10.1090/S0273-0979-1994-00511-7
MathSciNet review: 1256977
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Abstract: We announce the classification of two related classes of flag-transitive geometries. There is an infinite family of such geometries, related to the nonsplit extensions $ {3^{[\begin{array}{*{20}{c}} n \\ 2 \\ \end{array} ]}}^2 \cdot {\text{Sp}}_{2n}(2)$, and twelve sporadic examples coming from the simple groups $ {M_22}$, $ {M_23}$, $ {M_24}$, He, $ Co_{1}$, $ Co_{2}$, $ {J_4}$, BM, M and the nonsplit extensions $ 3 \cdot {M_22}$, $ {3^{23}} \cdot Co_{2}$, and $ {3^{4371}} \cdot BM$.


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DOI: https://doi.org/10.1090/S0273-0979-1994-00511-7
Article copyright: © Copyright 1994 American Mathematical Society

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