Automorphisms of Right-Angled Coxeter Groups

Mauricio Gutierrez and Anton Kaul

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-10

Abstract:

If ( ð ‘Š , 𠑆 ) is a right-angled Coxeter system, then A u t ( ð ‘Š ) is a semidirect product of the group A u t ∘ ( ð ‘Š ) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, A u t ∘ ( ð ‘Š ) is a semidirect product of I n n ( ð ‘Š ) by the quotient O u t ∘ ( ð ‘Š ) = A u t ∘ ( ð ‘Š ) / I n n ( ð ‘Š ) . 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 → I n n ( ð ‘Š ) → A u t ( ð ‘Š ) → O u t ( ð ‘Š ) → 1 and consequently, all group extensions 1 → ð ‘Š → ð º â†’ ð ‘„ → 1 are trivial.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:976390

DOI: 10.1155/2008/976390

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