Non-abelian representations of some sporadic geometries

For a point-line incidence system S = (P, L) with three points per line we define the universal representation group of S as R(S) = [z(p), p is an element of P \ z(p)(2) = 1 for p is an element of P, z(p)z(q)z(r) = 1 for {p,q,r} is an element of L]. We prove that if G is the 2-local parabolic geometry of the sporadic simple group F-1 (the Monster) or F-2 (the Baby Monster) then R(G) congruent to F-1 or 2 . F-2, respectively. (C) 1996 Academic Press, Inc.