"coset" meaning in English

See coset in All languages combined, or Wiktionary

Noun

Audio: LL-Q1860 (eng)-Flame, not lame-coset.wav Forms: cosets [plural]
Etymology: From co- + set; apparently first used 1910 by American mathematician George Abram Miller. Etymology templates: {{prefix|en|co|set}} co- + set Head templates: {{en-noun}} coset (plural cosets)
  1. (algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup. Wikipedia link: George Abram Miller, coset Categories (topical): Algebra, Group theory Derived forms: double coset, left coset, multicoset, right coset, supercoset Translations (result of applying group operation with fixed element from the parent group on each element of a subgroup): kõrvalklass (Estonian), sivuluokka (Finnish), mellékosztály (Hungarian), classe laterale [feminine] (Italian), warstwa [feminine] (Polish), classe lateral [feminine] (Portuguese), sidoklass [common-gender] (Swedish)

Inflected forms

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          "word": "double coset"
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          "word": "right coset"
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          "word": "supercoset"
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          "text": "1970 [Addison Wesley], Frederick W. Byron, Robert W. Fuller, Mathematics of Classical and Quantum Physics, Volumes 1-2, Dover, 1992, page 597,\nTheorem 10.5. The collection consisting of an invariant subgroup H and all its distinct cosets is itself a group, called the factor group of G, usually denoted by G/H. (Remember that the left and right cosets of an invariant subgroup are identical.) Multiplication of two cosets aH and bH is defined as the set of all distinct products z = xy, with x ∈ aH and y ∈ bH; the identity element of the factor group is the subgroup H itself."
        },
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          "text": "1982 [Stanley Thornes], Linda Bostock, Suzanne Chandler, C. Rourke, Further Pure Mathematics, Nelson Thornes, 2002 Reprint, page 614,\nIn general, the coset in row x consists of all the elements xh as h runs through the various elements of H."
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          "ref": "2009, Lindsay N. Childs, A Concrete Introduction to Higher Algebra, 3rd edition, Springer, page 231:",
          "text": "Example 3. Let G#x3D;#x5C;mathbb#x7B;Z#x7D; (the operation is #x2B;), H#x3D;2#x5C;mathbb#x7B;Z#x7D;. Then the coset 1#x2B;2#x5C;mathbb#x7B;Z#x7D; is the set of integers of the form 1#x2B;2k where k runs through all elements of #x5C;mathbb#x7B;Z#x7D;.",
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        }
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      "code": "et",
      "lang": "Estonian",
      "sense": "result of applying group operation with fixed element from the parent group on each element of a subgroup",
      "word": "kõrvalklass"
    },
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      "sense": "result of applying group operation with fixed element from the parent group on each element of a subgroup",
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    },
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      "sense": "result of applying group operation with fixed element from the parent group on each element of a subgroup",
      "word": "mellékosztály"
    },
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      "sense": "result of applying group operation with fixed element from the parent group on each element of a subgroup",
      "tags": [
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      "word": "classe laterale"
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  "word": "coset"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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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