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

Ivanov, A. A.; Shpectorov, S. V.

doi:10.1090/S0273-0979-1994-00511-7

The flag-transitive tilde and Petersen-type geometries are all known
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by A. A. Ivanov and S. V. Shpectorov PDF

Bull. Amer. Math. Soc. 31 (1994), 173-184 Request permission

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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