Etimology
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.
noun
group (plural groups)
A number of things or persons being in some relation to one another.
(group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
(geometry, archaic) An effective divisor on a curve.
A (usually small) group of people who perform music together.
(astronomy) A small number (up to about fifty) of galaxies that are near each other.
(chemistry) A column in the periodic table of chemical elements.
(chemistry) A functional group.
(sociology) A subset of a culture or of a society.
(military) An air force formation.
(geology) A collection of formations or rock strata.
(computing) A number of users with the same rights with respect to accession, modification, and execution of files, computers and peripherals.
An element of an espresso machine from which hot water pours into the portafilter.
(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.
(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.
(business) A commercial organization.
Examples
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 to say the last prayer.
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 is sorting pupils into ability groups by streaming or setting.
there is a group of houses behind the hill; he left town to join a Communist group
A group of people gathered in front of the Parliament to demonstrate against the Prime Minister's proposals.
Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem.
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 obtained by some "arithmetic" operations. One such construction we have already seen: if we choose all matrices of SL with integer coefficients, then the corresponding elements of PSL form the modular group PSL.
In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO group and its covering group SU.
Did you see the new jazz group?
Nitro is an electron-withdrawing group.
It is the third of eight matches that Spain will play in Group I, but the coach Vicente del Bosque has described it as being more akin to the first leg of a cup semi-final.
Related words
synonyms
(number of things or persons being in some relation to each other): collection, set
(people who perform music together): band, ensemble
See also Thesaurus:group
hypernyms
(in group theory): monoid
hyponyms
Abelian group
affinity group
battalion tactical group
Bianchi group
boy group
Einsatz group
encounter group
factor group
free group
fundamental group
general linear group
girl group
informal group
kinematic group
Kleinian group
Lie group
Local Group
minority group
moving group
p-group
play group
pop group
quotient group
rap group
simple group
status group
subgroup
sub-group
technical group
total group
triangle group
Tuesday Group
von Dyck group
we-group
youth group
verb
group (third-person singular simple present groups, present participle grouping, simple past and past participle grouped)
(transitive) To put together to form a group.
(intransitive) To come together to form a group.
Examples
group the dogs by hair colour
For many people forming pods last year, finding compatible people to group with was not a cost but a goal.
Related words
synonyms
(put together to form a group): amass, categorise/categorize, classify, collect, collect up, gather, gather together, gather up; see also Thesaurus:round up
(come together to form a group): assemble, begather, foregather, throng; see also Thesaurus:assemble