A Characterization of 3- Local Subgroups of Ly

In this paper we discuss an amalgam (M.. SL. (5)) of rank 2 and characteristic 3. Suppose G is a group generated by its two subgroups P. , P. and suppose P. , P. and their intersection satisfy some local group theoretic conditions. Then assuming that O³ (P./O. (P. )) and O³ ' (P. /O. (P. )) are isomorphic to M.. and SL. (5) respectively. we give an explicit description about the structures of O. (P.) and O. (P. ) 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.