Phrase guide

fundamental group

noun · 1 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.

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1

noun

Meaning 1

For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, topology

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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Across languages

Translations

14 source translations are retained for this English entry.

  • Catalan: grup fonamental — group of equivalence classes of the homotopies of loops in a given topological space
  • Czech: fundamentální grupa — group of equivalence classes of the homotopies of loops in a given topological space
  • Dutch: fundamentaalgroep — group of equivalence classes of the homotopies of loops in a given topological space
  • Finnish: perusryhmä — group of equivalence classes of the homotopies of loops in a given topological space
  • French: groupe fondamental — group of equivalence classes of the homotopies of loops in a given topological space
  • German: Fundamentalgruppe — group of equivalence classes of the homotopies of loops in a given topological space
  • Hungarian: fundamentális csoport — group of equivalence classes of the homotopies of loops in a given topological space
  • Icelandic: undirstöðugrúpa — group of equivalence classes of the homotopies of loops in a given topological space
  • Italian: gruppo fondamentale — group of equivalence classes of the homotopies of loops in a given topological space
  • Polish: grupa podstawowa — group of equivalence classes of the homotopies of loops in a given topological space
  • Russian: фундаментальная группа (fundamentalʹnaja gruppa) — group of equivalence classes of the homotopies of loops in a given topological space
  • Swedish: fundamentalgrupp — group of equivalence classes of the homotopies of loops in a given topological space
  • Turkish: temel grup — group of equivalence classes of the homotopies of loops in a given topological space
  • Ukrainian: фундаментальна група (fundamentalʹna hrupa) — group of equivalence classes of the homotopies of loops in a given topological space