Lie algebras and 3-transpositions
  We describe a construction of an algebra over the field of order 2 starting from a conjugacy class of 3-transpositions in a group. In particular, we determine which simple Lie algebras arise by this construction. Among other things, this construction yields a natural embedding of the sporadic simple group $\Fi{22}$ in the group $^2E_6(2)$. 
H. Cuypers, M. Horn, J. in 't panhuis, S. Shpectorov
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