期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/976390
出版社：Hindawi Publishing Corporation
摘要：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.
