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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 Fi22 in the group E62(2).
In the first part [C. Bennett, R. Gramlich, C. Hoffman, S. Shpectorov, Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 1: General simple connectedness, J. Algebra 312 (2007) 426–444], a characterization of central quotients of the group Spin(2n+1,q) is given for n⩾3 and all odd prime powers q, with the exception of the cases n=3, q∈{3,5,7,9}. The present article treats these...
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