Geodesic
Singular Isometries in Orthogonal Groups
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 189-198

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In this paper, we study the behaviour of singular isometries in orthogonal groups. These are isometries whose path is a singular subspace. We shall prove that the path of such a singular isometry is always even-dimensional. We shall use this result to show that the subgroup of the orthogonal group On(K, Q) which is generated by the singular isometries is the commutator subgroup Ωn(K, Q). 
Gunther, Georg. Singular Isometries in Orthogonal Groups. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 189-198. doi: 10.4153/CMB-1977-031-6
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     author = {Gunther, Georg},
     title = {Singular {Isometries} in {Orthogonal} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {189--198},
     year = {1977},
     volume = {20},
     number = {2},
     doi = {10.4153/CMB-1977-031-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-031-6/}
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