Abstract.
Most classical groups arising from (anti-) hermitian forms or (pseudo-) quadratic forms contain so-called isotropic transvections. The isotropic transvection subgroups of these classical groups, i.e., the subgroups generated by all isotropic transvections with a fixed axis, form a class Σ of abelian subgroups which is a class of abstract transvection groups in the sense of Timmesfeld [24]. In this paper we give a common characterization of all these classical groups with isotropic transvections as linear groups generated by a class Σ of abstract transvection groups such that the elements of A∈Σ are transvections.
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Oblatum 19-VI-1998 & 8-XII-1998 / Published online: 10 May 1999
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Cuypers, H., Steinbach, A. Linear transvection groups and embedded polar spaces . Invent. math. 137, 169–198 (1999). https://doi.org/10.1007/s002220050328
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DOI: https://doi.org/10.1007/s002220050328