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- ItemOn reflection subgroups of finite Coxeter groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, GerhardLet W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.