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- W49114214 abstract "The sporadic simple group F 2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry $$mathcal{G}(F_2 )$$ . P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let $$mathcal{K}$$ be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of $$mathcal{K}$$ is isomorphic to the corresponding residue in $$mathcal{G}(F_2 )$$ . We show that in this case $$mathcal{K}$$ is isomorphic to $$mathcal{G}(F_2 )$$ . This result realizes a step in classification of the flag-transitive P-geometries and also plays an important role in the characterization of the Fischer–Griess Monster in terms of its 2-local parabolic geometry." @default.
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- W49114214 date "1992-01-01" @default.
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- W49114214 doi "https://doi.org/10.1023/a:1022433314190" @default.
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