Geodesic
Linear representations of groups generated by reflections
Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 459-463 
O. V. Schwarzman. Linear representations of groups generated by reflections. Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 459-463. http://geodesic.mathdoc.fr/item/SM_1970_11_3_a10/
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_3_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following theorem is proved: two groups $\Gamma_1$ and $\Gamma_2$ acting discretely on $\Lambda^3$, with compact factor-space and isomorphic, as abstract groups, to a group generated by reflections, are conjugate in the group of motions of $\Lambda^3:g\Gamma_1g^{-1}=\Gamma_2$. Bibliography: 8 titles.

[1] A. Weyl, “On discrete subgroups of Lie groups”, Ann. Math., 72 (1960), 369–384 ; 75 (1962), 578–602 | DOI | MR | DOI | MR

[2] E. B. Vinberg, “Diskretnye gruppy, porozhdennye otrazheniyami v prostranstvakh Lobachevskogo”, Matem. sb., 72(114) (1967), 471–488 | MR | Zbl

[3] A. Selberg, “O diskretnykh gruppakh v mnogomernykh simmetrichnykh prostranstvakh”, Matematika, 6:3 (1962), 1–15 | MR

[4] S. Maklein, Gomologiya, Mir, Moskva, 1966

[5] S. Sternberg, Lectures on differential geometry, Englewood Cliffs, 1964 | MR | Zbl

[6] E. M. Andreev, “O vypuklykh mnogogrannikakh v prostranstvakh Lobachevskogo”, Matem. sb., 81(123) (1970), 446–478 | MR

[7] H. S. M. Coxeter, “Discrete groups generated by reflections”, Ann. Math., 35:3 (1934), 588–621 | DOI | MR | Zbl

[8] Zh. Adamar, Elementarnaya geometriya, t. 2, Uchpedgiz, Moskva, 1958