"automorphism group" meaning in All languages combined

See automorphism group on Wiktionary

Noun [English]

Forms: automorphism groups [plural]
Head templates: {{en-noun}} automorphism group (plural automorphism groups)
  1. (group theory) The group of automorphisms of a given set or other mathematical object, with the group operation being function composition. Wikipedia link: automorphism group Categories (topical): Group theory Synonyms (symmetric group): symmetry group (english: chiefly in geometry) Hyponyms: Galois group, general linear group, projective linear group Related terms: group automorphism (english: type of automorphism)

Inflected forms

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          "text": "The automorphism group of a set is the set's symmetric group.",
          "type": "example"
        },
        {
          "text": "The automorphism group of a finite-dimensional vector space (respectively, projective space) is the space's general linear group (respectively, projective linear group).",
          "type": "example"
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        {
          "ref": "1984, José M. Isidro, László L. Stachó, Holomorphic Automorphism Groups in Banach Spaces: An Elementary Introduction, Elsevier (North-Holland), page vi:",
          "text": "Moreover, we think that this approach to the automorphism groups of Banach space domains may also serve as motivating and illustrative material in introducing students to the theory of Lie groups and complex manifolds.",
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          "ref": "1993, Matatyahu Rubin, The Reconstruction of Trees from Their Automorphism Groups, American Mathematical Society, page 5:",
          "text": "Recently Droste, Holland and Macpherson in [DHM1], [DHM2] and [DHM3] investigated various questions concerning the automorphism groups of homogeneous #x5C;aleph#x5F;0-categorical trees.",
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          "ref": "2002, Masamichi Takesaki, Theory of Operator Algebras II, Springer, page 91:",
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        "(group theory) The group of automorphisms of a given set or other mathematical object, with the group operation being function composition."
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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