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Reflection subgroups of Coxeter systems. (English) Zbl 0712.20026
Let \((W,R)\) be a Coxeter system, \(T\) the set of reflections, \(W'=\langle W'\cap T\rangle\) a reflection subgroup. The author shows that a certain subset of \(T\) is a set of Coxeter generators of \(W'\). He also gives a geometric criterion for a set of reflections to be the set of canonical generators of a reflection subgroup and classifies the isomorphism types of reflection subgroups of affine Weyl groups.
Reviewer: E.W.Ellers

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20H15 Other geometric groups, including crystallographic groups
20F05 Generators, relations, and presentations of groups
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