Abstract
Suppose G is a subgroup of GL ( k ) , M a finite-dimensional vectorspace over the field k with char k ≠ 2 , generated by quadratic elements σ satisfying c ○ σ ∈ G for all c ∈ k ∗ . Then one can define root-subgroups of G intrinsically, i.e. just in terms of the quadratic elements. In this paper we determine such groups G generated by three root-subgroups, which do not contain a pair of commuting root-subgroups. This is a further step of the determination of groups G, when ( G , M ) is a quadratic pair.
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