Simple connectedness of the 3-local geometry of the Monster

[摘要] We consider the 3-local geometry M of the Monster group M introduced as a locally dual polar space of the group Omega(8)(-)(3) and independently in the context of minimal p-local parabolic geometries for sporadic simple groups. More recently the geometry appeared implicitly within the Z(3)-orbifold construction of the Moonshine module V. In this paper we prove the simple connectedness of M. This result makes unnecessary the refereeing to the classification of finite simple groups in the Z(3)-orbifold construction of V and realizes an important step in the classification of the flag-transitive c-extensions of the classical dual polar spaces. We make use of the simple connectedness results for the 2-local geometry of hi and for a subgeometry in M which is the 3-local geometry of the Fischer group M(24). (C) 1997 Academic Press.

[发布日期] 1997-08-15