扩展的F_4-建筑物和小怪物
Extended F_4-buildings and the Baby Monster
摘要：
Baby Monster群B自然地作用于图c.F_4（t）（t=4）的几何E（B），并且B对E（B）的作用是旗传递的.它具有以下性质：（a）任何两个类型1的元素最多与一个类型2的公共元素关联，（b）三个类型1的元素成对地与类型2的公共元素关联，当且仅当它们与类型5的公共元素关联。证明了E（B）是唯一的（非必要的旗传递的）c.F_4（t）-几何，满足t=4，（a）和（b），从而得到了B的第一个关联几何刻画，类似于已知的作用于建筑物的典型群.进一步证明了E（B）包含子几何E（^2E_6（2））和E（Fi 22），图为c.F_4（2）和c.F_4（1）.这些子几何的稳定子分别诱导了^2E_6（2）：2和Fi 22：2的旗传递作用量。进一步构造了t=2的具有旗传递自同构群的三个例子。本文给出了满足（a）和（b）的任意c.F_4（t）中距离为2的一对顶点的公共邻域所诱导的子图同构类型的可能性的完整列表。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
