Mathematics – Group Theory
Scientific paper
2005-01-18
Communications in Algebra, 34 (2006) No.7, pp.2559-2595
Mathematics
Group Theory
30 pages
Scientific paper
10.1080/00927870600651281
In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.
No associations
LandOfFree
On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-705303