Li Huiling, Huang Jianhua
In this paper we discuss an amalgam (M11, SL2 (5)) of rank 2 and characteristic 3. Suppose G is a group generated by its two subgroups P1, P2, and suppose P1, P2 and their intersection satisfy some local group-theoretic conditions. Then, assuming that O3 (P1/O3(P1)) and O3′ (P2/O3(P2)) are isomorphic to M11 and SL2 (5) respectively, we give an explicit description about the structures of O3 (P1) and O3 (P2) and of the operations of Pi's on them. At this time, they have structures similar to those of some 3-local subgroups of the sporadic simple group Ly.