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Coxeter group

Coxeter group noun: any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

Noun

Coxeter group (plural Coxeter groups)

  1. Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.
    • We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group.1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. de Clerck, editors, Finite Geometries and Combinatorics, page 277
    • The above definitions, of Cayley graph, reflection, wall, half-space, folding, Bruhat order, etc., work for any Coxeter group.2007, Michael B. Smythe, Julian Webster, “12: Discrete Spatial Models”, in Marco Aiello, Ian Pratt-Hartmann, Johan van Benthem, editors, Handbook of Spatial Logics, page 795

Forms of Coxeter group

pluralCoxeter groups

Origin of Coxeter group

Named for British-born Canadian mathematician H. S. M. Coxeter (1907–2003).

Questions about Coxeter group

What does Coxeter group mean?
Coxeter group means any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.
What part of speech is Coxeter group?
Coxeter group is a noun.
What is the plural of Coxeter group?
The plural of Coxeter group is Coxeter groups.

Words near Coxeter group in the dictionary

  1. Coxeter
  2. Coxeter diagram
  3. Coxeter diagrams
  4. Coxeter graph
  5. Coxeter graphs
  6. Coxeter group
  7. Coxeter groups
  8. Coxeter matrix
  9. Coxeter matrixes
  10. Coxeter-Dynkin diagram
  11. Coxeter-Dynkin diagrams

Source and license

Adapted from Wiktionary: Coxeter group (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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