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.
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