Phrase guide

automorphism 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

The group of automorphisms of a given set or other mathematical object, with the group operation being function composition.

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

Examples

  • The automorphism group of a set is the set's symmetric group.
  • The automorphism group of a finite-dimensional vector space (respectively, projective space) is the space's general linear group (respectively, projective linear group).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

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Across languages

Translations

1 source translations are retained for this English entry.

  • Polish: grupa automorfizmów — group whose elements are the automorphisms of a given mathematical object