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group

From Wiktionary, the free dictionary
See also: Group

English

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Alternative forms

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Etymology

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From French groupe (“cluster, group”), from Italian gruppo, groppo (“a knot, heap, group, bag (of money)”), from Vulgar Latin *cruppo, Renaissance Latin grupus, from Frankish *krupp, from Proto-Germanic *kruppaz (“lump, round mass, body, crop”), from Proto-Indo-European *grewb- (“to crumple, bend, crawl”). In the sense of group theory coined (in French, as groupe) by Évariste Galois.

Cognate with German Kropf (“crop, craw, bunch”); Old English cropp, croppa (“cluster, bunch, sprout, flower, berry, ear of corn, crop”) (whence English crop); Dutch krop (“craw”), Icelandic kroppr (“hump, bunch”). Doublet of crop and croup.

Pronunciation

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  • enPR: gro͞op, IPA(key): /ɡɹuːp/
  • Audio (US):(file)
  • Rhymes: -uːp

Noun

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group (plural groups)

  3. (group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
    • 1977, Roger C. Lyndon, Paul E. Schupp, Combinatorial Group Theory, Springer, page 192:
      Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem.
    • 1992, Svetlana Katok, Fuchsian Groups, University of Chicago Press, page 112:
      In this chapter we give some examples of Fuchsian groups. The most interesting and important ones are the so-called "arithmetic" Fuchsian groups, i.e., discrete subgroups of PSL(2,R) obtained by some "arithmetic" operations. One such construction we have already seen: if we choose all matrices of SL(2,R) with integer coefficients, then the corresponding elements of PSL(2,R) form the modular group PSL(2,Z).
    • 2007, Zhong-Qi Ma, Group Theory for Physicists, World Scientific, page 277,
      In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO(3) group and its covering group SU(2).
  5. (geometry, archaic) An effective divisor on a curve.
  7. A (usually small) group of people who perform music together.
    Did you see the new jazz group?
  9. (astronomy) A small number (up to about fifty) of galaxies that are near each other.
  11. (chemistry) A column in the periodic table of chemical elements.
  13. (chemistry) A functional group.
    Nitro is an electron-withdrawing group.
  15. (sociology) A subset of a culture or of a society.
  17. (military) An air force formation.
  19. (geology) A collection of formations or rock strata.
  21. (computing) A number of users with the same rights with respect to accession, modification, and execution of files, computers and peripherals.
  23. An element of an espresso machine from which hot water pours into the portafilter.
  25. (music) A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.
  27. (sports) A set of teams playing each other in the same division, while not during the same period playing any teams that belong to other sets in the division.
  29. (business) A commercial organization.

Synonyms

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Hypernyms

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Hyponyms

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Derived terms

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some unsorted (may also be hyponyms)

Descendants

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  • → Gulf Arabic: قروب (grūp)
  • → Japanese: グループ (gurūpu)
  • → Korean: 그룹 (geurup)
  • → Tongan: kulupu

Translations

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References

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Verb

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group (third-person singular simple present groups, present participle grouping, simple past and past participle grouped)

  1. (transitive) To put together to form a group.
    group the dogs by hair colour
  2. (intransitive) To come together to form a group.
    • 2021 October 1, Calder Katyal, “Schools Need to Undo the Damage of Pods”, in The Atlantic‎[1]:
      For many people forming pods last year, finding compatible people to group with was not a cost but a goal.

Synonyms

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Derived terms

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Translations

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Further reading

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Chinese

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Etymology

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From English group. Doublet of 谷.

Pronunciation

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Noun

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group (Hong Kong Cantonese)

  1. group of people or objects (Classifier: 個／个 c)
  2. (social media) group

Classifier

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group (Hong Kong Cantonese)

  1. Classifier for groups of people or objects..
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