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In this chapter we will describe the classification of groups G generated by a class of abstract root subgroups. This classification which is relatively long and difficult, works in principal as follows: First one constructs from the group-theoretic conditions a point-line geometry, which is either a polar space, a projective space, a generalized n-gon or a parapolar space. Then one uses certain geometric classifications of these geometries, i.e. theorems showing that under some additional conditions the flag complex of these geometries is a spherical building. Finally, to determine the group, one shows that the abstract root subgroups act as (centers) of long root subgroups on this building, whence G is the uniquely determined normal subgroup of the automorphism group of the building generated by the class of (centers) of the long root subgroups.
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