Möbius group

noun

The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere.

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Meanings

nounMöbius group (plural Möbius groups)

plural Möbius groups · alternative Moebius group · alternative Mobius group

  1. group theoryThe projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere.
  2. group theoryFor a given dimension n, the group of projective transformations leaving a particular hypersphere invariant.

Synonyms & antonyms

Broader
Lie group

Origin

Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.

Full word history & related roots →

Translations

Dutch Möbius-groep
  • Möbius-groepPGL(2,C)
Polish grupa homograficzna
  • grupa homograficznaPGL(2,C)
Spanish grupo de Möbius
  • grupo de MöbiusPGL(2,C)
Cite this entry
APA

Möbius group. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/M%C3%B6bius%20group

MLA

“Möbius group.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/M%C3%B6bius%20group. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Möbius group,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/M%C3%B6bius%20group.

Source: Möbius group on Wiktionary, CC BY-SA 4.0.