Geodesic
Genus of elements of orthogonal groups
Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 695-702 
G. V. Matveev. Genus of elements of orthogonal groups. Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 695-702. http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a7/
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     author = {G. V. Matveev},
     title = {Genus of elements of orthogonal groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {695--702},
     year = {1973},
     volume = {13},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the number of classes in the genus of an element of an orthogonal group can take arbitrarily large values.