On Reflection Subgroups of Finite Coxeter Groups

J. Matthew Douglass; Götz Pfeiffer; Gerhard Röhrle

doi:10.1080/00927872.2012.661005

On Reflection Subgroups of Finite Coxeter Groups

J. Matthew Douglass
, Götz Pfeiffer
, Gerhard Röhrle

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

16 Citations (Scopus)

Abstract

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.

Original language	English
Pages (from-to)	2574-2592
Number of pages	19
Journal	Communications in Algebra
Volume	41
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2012.661005
Publication status	Published - 2013

Keywords

Coxeter elements
Finite Coxeter groups
Reflection subgroups

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10.1080/00927872.2012.661005

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title = "On Reflection Subgroups of Finite Coxeter Groups",

abstract = "Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.",

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AU - Douglass, J. Matthew

AU - Pfeiffer, Götz

AU - Röhrle, Gerhard

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AB - Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.

KW - Coxeter elements

KW - Finite Coxeter groups

KW - Reflection subgroups

UR - https://www.scopus.com/pages/publications/84879659798

U2 - 10.1080/00927872.2012.661005

DO - 10.1080/00927872.2012.661005

M3 - Article

SN - 0092-7872

VL - 41

SP - 2574

EP - 2592

JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

On Reflection Subgroups of Finite Coxeter Groups

Abstract

Keywords

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