group

A number of things or persons being in some relation to one another.

Noun

  1. A number of things or persons being in some relation to one another.
    • Then everybody once more knelt, and soon the blessing was pronounced. The choir and the clergy trooped out slowly, […], down the nave to the western door. […] At a seemingly immense distance the surpliced group stopped...
    • Imagine a country where children do nothing but play until they start compulsory schooling at age seven. Then, without exception, they attend comprehensives until the age of 16. Charging school fees is illegal, and so...
    • there is a group of houses behind the hill; he left town to join a Communist group
  2. A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
    • Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem. - 1977, Roger C. Lyndon, Paul E. Schupp, Combinatorial Group Theory, Springer, page 192:
    • 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"...
    • 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).
  3. An effective divisor on a curve.
  4. A (usually small) group of people who perform music together.
    • Did you see the new jazz group?
  5. A small number (up to about fifty) of galaxies that are near each other.
  6. A column in the periodic table of chemical elements.

    Coordinate Terms: period

  7. A functional group.
    • Nitro is an electron-withdrawing group.
  8. A subset of a culture or of a society.
  9. An air force formation.
  10. A collection of formations or rock strata.
  11. A number of users with the same rights with respect to accession, modification, and execution of files, computers and peripherals.
  12. An element of an espresso machine from which hot water pours into the portafilter.

Origin

Etymology tree Proto-Indo-European *grewbʰ-der. Proto-Germanic *kruppazder. Frankish *kruppbor. Vulgar Latin *cruppus Italian gruppobor. French groupebor. ▲ Italian gruppobor. English group From French groupe (“cluster, group”), from Italian gruppo, groppo (“a knot, heap, group, bag (of money)”). In the "group theory" sense, calqued from French groupe, a term coined by the young French mathematician Évariste Galois in 1830. 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.

Forms

groups groop groupe

Wikipedia

group theory

Synonyms

collection set band ensemble group

Antonyms

individual monad union unity

Hypernyms

monoid

Hyponyms

Abelian group affinity group battalion tactical group Bianchi group book discussion group book group boy group Einsatz group encounter group factor group free group fundamental group general linear group girl group group of galaxies informal group kinematic group Kleinian group Lie group Local Group minority group moving group p-group play group

Derived

abelian group ABO group action group activity group psychotherapy additive group advocacy group affine group age group airgroup algebraic fundamental group algebraic group allogroup alternating group automorphism group baby monster group battlegroup biogroup block group blood group boron group boundary group braid group Brauer group breakout group

Verb

  1. To put together to form a group.
    • group the dogs by hair colour
  2. To come together to form a group.
    • For many people forming pods last year, finding compatible people to group with was not a cost but a goal. - 2021 October 1, Calder Katyal, “Schools Need to Undo the Damage of Pods”, in The Atlantic:
  3. To eliminate in the group stage of a competition.
    • Clubs like Real Sociedad are getting grouped in the Europa League. Even clubs like Atletico Madrid and Villareal are finding it hard to progress to the R16 in the UCL. - 2022 April 5, leocic (@leocitic), “leocic on...

Forms

groups grouping grouped groop groupe

Synonyms

amass categorise categorize classify collect collect up gather gather together gather up assemble begather foregather throng

Derived

groupable