TY - JOUR

T1 - On the direct indecomposability of infinite irreducible coxeter groups and the isomorphism problem of coxeter groups

AU - Nuida, Koji

N1 - Funding Information:
The author is supported by JSPS Research Fellowship (No. 16-10825).

PY - 2006/6/1

Y1 - 2006/6/1

N2 - In this article, we prove that any irreducible Coxeter group of infinite order, which is possibly of infinite rank, is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involu-tions. As a consequence, the problem of deciding whether two general Coxeter groups are isomorphic is reduced to the case of irreducible ones. We also describe the automorphism group of a general Coxeter group in terms of those of its irreducible components.

AB - In this article, we prove that any irreducible Coxeter group of infinite order, which is possibly of infinite rank, is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involu-tions. As a consequence, the problem of deciding whether two general Coxeter groups are isomorphic is reduced to the case of irreducible ones. We also describe the automorphism group of a general Coxeter group in terms of those of its irreducible components.

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U2 - 10.1080/00927870600651281

DO - 10.1080/00927870600651281

M3 - Article

AN - SCOPUS:33745612723

VL - 34

SP - 2559

EP - 2595

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 7

ER -