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2007 Matching theorems for systems of a finitely generated Coxeter group
Michael Mihalik, John G Ratcliffe, Steven T Tschantz
Algebr. Geom. Topol. 7(2): 919-956 (2007). DOI: 10.2140/agt.2007.7.919

Abstract

We study the relationship between two sets S and S of Coxeter generators of a finitely generated Coxeter group W by proving a series of theorems that identify common features of S and S. We describe an algorithm for constructing from any set of Coxeter generators S of W a set of Coxeter generators R of maximum rank for W.

A subset C of S is called complete if any two elements of C generate a finite group. We prove that if S and S have maximum rank, then there is a bijection between the complete subsets of S and the complete subsets of S so that corresponding subsets generate isomorphic Coxeter systems. In particular, the Coxeter matrices of (W,S) and (W,S) have the same multiset of entries.

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Michael Mihalik. John G Ratcliffe. Steven T Tschantz. "Matching theorems for systems of a finitely generated Coxeter group." Algebr. Geom. Topol. 7 (2) 919 - 956, 2007. https://doi.org/10.2140/agt.2007.7.919

Information

Received: 31 March 2006; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1134.20045
MathSciNet: MR2336245
Digital Object Identifier: 10.2140/agt.2007.7.919

Keywords: Coxeter groups

Rights: Copyright © 2007 Mathematical Sciences Publishers

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