Geodesic
Reflection subgroups of Euclidean reflection groups
Sbornik. Mathematics, Tome 196 (2005) no. 9, pp. 1349-1369 Cet article a éte moissonné depuis la source Math-Net.Ru

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The subgroups of discrete Euclidean groups generated by reflections are classified. 
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P. V. Tumarkin; A. A. Felikson. Reflection subgroups of Euclidean reflection groups. Sbornik. Mathematics, Tome 196 (2005) no. 9, pp. 1349-1369. http://geodesic.mathdoc.fr/item/SM_2005_196_9_a4/

[1] Dynkin E. B., “Poluprostye podalgebry poluprostykh algebr Li”, Matem. sb. Nov. ser., 30:2 (1952), 349–462 | MR | Zbl

[2] Felikson A., “Koksterovskie razbieniya giperbolicheskikh simpleksov”, Matem. sb., 193:12 (2002), 134–156 | MR | Zbl

[3] Felikson A., “Koksterovskie razbieniya giperbolicheskikh tetraedrov”, Fundament. i prikl. matem., 9:1 (2003), 263–275 | MR

[4] Johnson N. W., Kellerhals R., Ratcliffe J. G., Tschantz S. T., “Commensurability classes of hyperbolic Coxeter groups”, Linear Algebra Appl., 345 (2002), 119–147 | DOI | MR | Zbl

[5] Klimenko E., Sakuma M., “Two-generator discrete subgroups of $\operatorname{Isom}(\mathbb H^2)$ containing orientation-reversing elements”, Geom. Dedicata, 72 (1998), 247–282 | DOI | MR | Zbl

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

[7] Vinberg E. B., Shvartsman O. V., “Diskretnye gruppy dvizhenii prostranstv postoyannoi krivizny”, Itogi nauki i tekhniki. Sovrem. problemy matem. Fundament. napravleniya, 29, VINITI, M., 1988, 147–259

[8] Kats V., Beskonechnomernye algebry Li, Mir, M., 1993 | MR | Zbl

[9] Burbaki N., Gruppy i algebry Li, gl. IV–VI, Mir, M., 1972 | MR | Zbl

[10] Onishchik A. L., “Comments on the paper “Semisimple subalgebras of semisimple Lie algebras””, Selected papers of E. B. Dynkin with commentary, Amer. Math. Soc., Providence, RI; International Press, Cambridge, MA, 2000 | Zbl

[11] Felikson A., “Koksterovskie razbieniya sfericheskikh simpleksov s nerazrezannymi dvugrannymi uglami”, UMN, 57:2 (2002), 201–202 | MR | Zbl

[12] Charney R., Davis M. W., “When is a Coxeter system determined by its Coxeter group?”, J. London Math. Soc. (2), 61:2 (2000), 441–461 | DOI | MR | Zbl