Automorphisms of Right-Angled Coxeter Groups
If (𝑊,𝑆) is a right-angled Coxeter system, then Aut(𝑊) is a semidirect product of the group Aut∘(𝑊) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut∘(𝑊) is a semidirect product of Inn(𝑊) by the quotient Out∘(𝑊)=Aut∘(𝑊)/Inn(𝑊). We al...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/976390 |
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| Summary: | If (𝑊,𝑆) is a right-angled Coxeter system, then Aut(𝑊) is a semidirect product of the group Aut∘(𝑊) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut∘(𝑊) is a semidirect product of Inn(𝑊) by the quotient Out∘(𝑊)=Aut∘(𝑊)/Inn(𝑊). We also give sufficient conditions for the compatibility of the two semidirect products. When this occurs there is an induced splitting of the sequence 1→Inn(𝑊)→Aut(𝑊)→Out(𝑊)→1 and consequently, all group extensions 1→𝑊→𝐺→𝑄→1 are trivial. |
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| ISSN: | 0161-1712 1687-0425 |