# On the regularity of the finite reflection groups

## Author

**R. B. Howlett** and **Jian-yi Shi**

## Status

Research Report 98-7

Date: 17 March 1998

## Abstract

We show that an irreducible finite reflection group G of rank greater than 1
is regular if and only if the associated root system is perfect. This holds
if and only if G is a Coxeter group. Hence we get a characterization of
Coxeter groups among all the irreducible finite reflection groups of rank
greater than 1.

## Key phrases

finite reflection groups. Coxeter groups. root systems.

## AMS Subject Classification (1991)

Primary: 20H15

Secondary: 20F55

## Content

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Sydney Mathematics and Statistics