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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

##### MSC:
 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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##### References:
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