Geodesic
A geometric characterization of Fischer's Baby Monster
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 45-69.

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Summary: The sporadic simple group $F _{2}$ known as Fischer's Baby Monster acts flag-transitively on a rank $5 P$-geometry $G( F _{2} )$ mathcalG(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 $K$ mathcalK be a flag-transitive $P$-geometry of rank 5. Suppose that each proper residue of $K$ mathcalK is isomorphic to the corresponding residue in $G( F _{2} )$ mathcalG(F_2 ) . We show that in this case $K$ mathcalK is isomorphic to $G( F _{2} )$ mathcalG(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.
Keywords: sporadic group, diagram geometry, simple connectedness, amalgams of groups 
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Ivanov, Alexander A. A geometric characterization of Fischer's Baby Monster. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 1, pp. 45-69. http://geodesic.mathdoc.fr/item/JAC_1992__1_1_a2/