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group

group

50 8.6
In mathematics, a set of elements with a rule for combining them that has an identity and inverses
  • noun
  • /ɡruːp/
  • Specialized
translation icon : grupo
  • When studying transformations, it's essential to determine whether the set behaves like a group under the defined operation.

Those are the designations of these Lie groups.

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Examples

  • One, find all the simple groups, and two, find all of the ways to combine them.

  • There were two groups, an experimental group (N=28) and a control group (N=29).

    Academic text (2008)
  • We work in separate groups.

  • I'm gonna split you up into groups of four.

  • In some studies, the tables are turned, and the experimental groups receive less than the control groups.

    Academic text (2008)
  • He was part of the control group.

  • Results indicated those in the experimental group learned to read more efficiently than those in the control group.

    Academic text (2015)
  • As they got closer to it, a big group of green-and-red birds flew overhead.

    Fiction book (1999)
  • We took the elevators down to the basement, where the physics group had its offices and laboratories.

    Fiction book (2000)
  • Asians and Pacific Islanders will continue to be the fastest growing ethnic groups in the United States.

    Academic text (1999)

Synonyms

mathematical group
vsgroup
  • Specialized
9.9

A collection of items with a rule to combine them, a do-nothing element, and opposites

has identical meaning but is the standard academic term in algebra

Idioms

72 2.3

Together, all people act or decide as one

Compounds

66 2.8

A group of people who meet regularly to give each other help and advice about a shared problem

59 2.2

People of about the same age that researchers study together for social or statistical reasons

58 2.8

People who share the same culture, language, or family history

57 4.9

A group that uses violence and fear against civilians to reach political goals

A group of people with the same goal who try to influence public decisions

group O
  • Specialized
47 3.7

A blood type with no A or B markers that can be given to most people

A group that tries to persuade people in power to change laws or rules for a cause

32 2.8

A group of people who meet regularly to learn and talk about school or course material

People who like each other and spend time together

group therapy
  • Specialized
18 3.4

A small group that meets with a therapist to talk about personal problems

A group of people who try to influence government decisions about one issue

13 2.6

A temporary team of people who work together to reach a clear goal

12 2.7

People who meet, talk, and feel they belong together

12 2.1

A band of musicians who play rock music

10 3.5

A small group of people who are most important in a larger organization or activity

9 5.0

A small group of people with more money, power, or education than others

9 3.2

A group of people of similar age or background who influence each other

A planned time when several people come together to talk about something

A small group that leaves a larger group because its members disagree

battle group
  • Specialized
5 4.7

A group of troops from different countries ready to move quickly to a crisis

4 4.1

A group that tries to change government decisions to help a cause or its members

4 3.9

A group that tries to persuade government officials to support laws or policies

People who play music together for a crowd

risk group
  • Specialized
4 3.6

People who are more likely to get a disease or be harmed

A group of people who follow strict religious rules and reject modern ideas

A group that tries to influence government decisions often by talking to politicians

A conversation among several people about one topic to share ideas or make a decision

3 2.3

A group of singers or musicians who play popular songs

group dynamics
  • Specialized
3 5.4

The way people in a group behave and interact

blood group
  • Specialized
2 3.2

A set of blood types people inherit from their parents that shows which blood they can receive

A unit of soldiers organized to do a specific job for the armed forces

battle group
  • Specialized
2 4.7

A military unit made of several groups of soldiers formed to fight

2 7.7

A senior officer in the Royal Air Force with the same rank as an army colonel

group insurance
  • Specialized
2 3.1

A company plan that helps employees pay medical or accident costs, usually cheaper than individual plans

2 2.0

A small informal group where young children meet to play and learn

1 2.0

A number of animals seen together as one unit, like a herd

group practice
  • Specialized
1 3.6

A clinic where several doctors share space, costs, and staff

1 2.1

A small group of musicians who play jazz together

A group of people who try to change or remove a government by force

1 1.8

A local group of young people who learn camping and teamwork

group A
  • Specialized
1 3.3

A blood type whose red blood cells have A markers

air group
  • Jargon
1 5.4

A unit of the United States Air Force larger than a squadron and smaller than a wing

Islamic Group
  • Offensive
1 8.7

An armed organization from Egypt that uses violence for political and religious aims

1 3.5

A small group inside an organization that works on a specific topic or project, not for politics

chemical group
  • Specialized
1 3.5

A small group of atoms joined together that is part of a larger molecule and gives it certain properties

encounter group
  • Specialized
1 8.3

A group meeting where people honestly talk about their feelings to understand themselves and each other

An armed group from Libya formed in 1995 that was against the government and joined al-Qaeda

linkage group
  • Specialized
1 7.2

A group of genes on the same chromosome that parents often pass together to their children

methyl group
  • Specialized
1 5.3

A small group of atoms in a molecule with one carbon and three hydrogen atoms

group theory
  • Specialized
1 7.4

A part of math that studies how things combine and their rules

group B
  • Specialized
1 4.6

A blood type with the B marker on red blood cells

A group of people who do the same job

taxonomic group
  • Specialized
1 7.0

A set of living things that are put together because they are related, for example lions and tigers

skiffle group
  • Archaic
1 8.1

A small band that plays folk and blues songs with guitars and homemade instruments

benzoyl group
  • Specialized
8.5

A part of a molecule with a six-carbon ring and a CO group that joins other atoms

benzyl group
  • Specialized
7.4

A part of a molecule made from toluene when one hydrogen is removed from its methyl group

Bill W. group
  • Jargon
5.9

A support group for people trying to stop drinking or using drugs

Bloomsbury Group
  • Literature
8.8

A group of English writers, thinkers, and artists from the early 1900s with new social and artistic ideas

biological group
  • Specialized
3.4

A group of plants or animals put together because they share traits

cacodyl group
  • Specialized
9.9

A part of a molecule where arsenic is attached to two small carbon-based groups

carbon group element
  • Specialized
6.7

A type of atom like carbon, silicon, tin, or lead found in Group 14 of the periodic table

carboxyl group
  • Specialized
4.9

A group of atoms with one carbon, two oxygens and one hydrogen that makes a molecule acidic

carbonyl group
  • Specialized
6.3

A part of a molecule where carbon joins oxygen by a double bond, found in aldehydes and ketones

commutative group
  • Specialized
8.4

A set with a rule to combine items where the order does not matter

cyano group
  • Specialized
7.0

A small part of a molecule with one carbon joined to one nitrogen by three bonds written −CN

cyanide group
  • Specialized
6.4

A small group of one carbon and one nitrogen atom, written -CN, found in many chemicals and often poisonous

Abelian group
  • Specialized
9.9

A set with a combining rule where order does not change the result

3.4

A system dividing human blood into A, B, AB and O groups by A and B substances on red cells

ABO group
  • Specialized
3.7

A system that divides blood into A, B, AB, and O by A and B proteins on red blood cells

acetyl group
  • Specialized
7.2

A small chemical part with atoms CH3CO that attaches to other molecules

acyl group
  • Specialized
8.4

A chemical part made when a carboxylic acid loses its OH group

adapid group
  • Specialized
9.9

An extinct group of small animals related to lemurs that lived 30 to 50 million years ago

amino group
  • Specialized
4.4

A group of atoms with a nitrogen atom and two hydrogen atoms that joins other molecules

Surface Forms

group singular
groups plural

Etymology

Group in mathematics keeps the same 'bunch' idea from the old root kruppa: it is a set of elements 'gathered' so they follow the same rules. That is why a mathematical group is treated as one organized unit.