Geodesic
Strong Tits Alternative for Subgroups of Coxeter Groups
Guennadi A Noskov1 ; Ernest B. Vinberg2, 3, 4
1Institute of Mathematics, Pevtsova 13, Omsk 644099, Russia
2Dept. of Algebra, Moscow State University, Moscow 119899, Russia
3It is proved that any subgroup of a Coxeter group has a finite index subgroup which either is abelian, or has a non-abelian free quotient.
4[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 259-264 
Guennadi A Noskov; Ernest B. Vinberg. Strong Tits Alternative for Subgroups of Coxeter Groups. Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 259-264. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a12/
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     author = {Guennadi A Noskov and Ernest B. Vinberg},
     title = {Strong {Tits} {Alternative} for {Subgroups} of {Coxeter} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {259--264},
     year = {2002},
     volume = {12},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a12/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

It is proved that any subgroup of a Coxeter group has a finite index subgroup which either is abelian, or has a non-abelian free quotient.