Mathematics – Group Theory
Scientific paper
2000-12-29
Invent. Math. 144(2001) 399-433
Mathematics
Group Theory
to appear in Inventiones Mathematicae
Scientific paper
10.1007/PL00005804
The Baby Monster group B acts naturally on a geometry E(B) with diagram c.F_4(t) for t=4 and the action of B on E(B) is flag-transitive. It possesses the following properties: (a) any two elements of type 1 are incident to at most one common element of type 2, and (b) three elements of type 1 are pairwise incident to common elements of type 2 iff they are incident to a common element of type 5. It is shown that E(B) is the only (non-necessary flag-transitive) c.F_4(t)-geometry, satisfying t=4, (a) and (b), thus obtaining the first characterization of B in terms of an incidence geometry, similar in vein to one known for classical groups acting on buildings. Further, it is shown that E(B) contains subgeometries E(^2E_6(2)) and E(Fi22) with diagrams c.F_4(2) and c.F_4(1). The stabilizers of these subgeometries induce on them flag-transitive actions of ^2E_6(2):2 and Fi22:2, respectively. Three further examples for t=2 with flag-transitive automorphism groups are constructed. A complete list of possibilities for the isomorphism type of the subgraph induced by the common neighbours of a pair of vertices at distance 2 in an arbitrary c.F_4(t) satisfying (a) and (b) is obtained.
Ivanov Anatoly A.
Pasechnik Dmitrii V.
Shpectorov S. V.
No associations
LandOfFree
Extended F_4-buildings and the Baby Monster does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extended F_4-buildings and the Baby Monster, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extended F_4-buildings and the Baby Monster will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-233606