group

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 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 is/are gathering in front of the Parliament to demonstrate against the Prime Minister's proposals.”

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.”

   “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).”

3. (archaic)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.
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.
13. 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.
14. 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.

    “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.”

15. A commercial organization.
16. (uncountable)Group therapy.

    “Aside from occasional moments of belligerence, he was a pretty affable guy. I rather liked him and, I guess, wanted him to like me. But his affability also included the odd "faggot" joke, which left me dubious over talking with him about being gay, even in "group."”

verb

1. (transitive)To put together to form a group.

   “group the dogs by hair colour”

2. (intransitive)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.”

3. (transitive)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.”