Phrase guide

Möbius group

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant.

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

3 source translations are retained for this English entry.

  • Dutch: Möbius-groep — PGL(2,C)
  • Polish: grupa homograficzna — PGL(2,C)
  • Spanish: grupo de Möbius — PGL(2,C)