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group

group

3 8.6
In mathematics, a set of elements with a rule for combining them that has an identity and inverses
  • noun
  • /ɡruːp/
  • Specialized
: 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
1 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

64 2.3

Together, all people act or decide as one

Compounds

81 2.8

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

72 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

61 2.2

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

61 2.8

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

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

People who like each other and spend time together

38 2.8

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

25 2.6

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

group therapy
  • Specialized
23 3.4

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

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

18 2.7

People who meet, talk, and feel they belong together

15 2.1

A band of musicians who play rock music

15 3.9

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

Islamic Group
  • Offensive
14 8.7

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

13 3.2

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

12 3.5

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

battle group
  • Specialized
11 4.7

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

11 5.0

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

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

8 4.1

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

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

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

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

risk group
  • Specialized
5 3.6

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

People who play music together for a crowd

group insurance
  • Specialized
4 3.1

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

4 2.3

A group of singers or musicians who play popular songs

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

blood group
  • Specialized
3 3.2

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

3 3.5

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

3 2.0

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

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

group dynamics
  • Specialized
3 5.4

The way people in a group behave and interact

2 2.1

A small group of musicians who play jazz together

2 1.8

A local group of young people who learn camping and teamwork

2 2.0

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

air group
  • Jargon
2 5.4

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

2 7.7

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

group practice
  • Specialized
2 3.6

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

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

encounter group
  • Specialized
1 8.3

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

1 3.4

An action done together by several people to reach the same goal

group B
  • Specialized
1 4.6

A blood type with the B marker on red blood cells

An armed group from Libya linked to al-Qaeda that uses violence to oppose Qaddafi

group theory
  • Specialized
1 7.4

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

1 9.9

A former Algerian Islamist militant group that carried out terrorist attacks to try to overthrow the government

group O
  • Specialized
1 3.7

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

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

All members take part in an activity or decision together

A group of people who do the same job

1 9.3

A group of Islamic extremists in Algeria that uses violent attacks to try to make an Islamic state

methyl group
  • Specialized
1 5.3

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

taxonomic group
  • Specialized
1 7.0

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

hydroxyl group
  • Specialized
1 6.5

A part of a molecule with one oxygen and one hydrogen atom found in alcohols

battle group
  • Specialized
1 4.7

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

carboxyl group
  • Specialized
1 4.9

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

skiffle group
  • Archaic
1 8.1

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

linkage group
  • Specialized
1 7.2

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

A group of people who meet to talk about their feelings with a trained therapist

group A
  • Specialized
1 3.3

A blood type whose red blood cells have A markers

group psychotherapy
  • Specialized
1 5.2

A therapy where a small group meets with a therapist to talk about problems

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

Bloomsbury Group
  • Literature
1 8.8

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

An Algerian extremist Islamist group that split from another militant group and tried to overthrow the government while supporting al-Qaeda

amino group
  • Specialized
1 4.4

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

carbonyl group
  • Specialized
1 6.3

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

1 4.5

A group of people who are related by blood or marriage

ABO group
  • Specialized
1 3.7

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

Abelian group
  • Specialized
1 9.9

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

alkyl group
  • Specialized
1 6.5

A part of a molecule made of carbon and hydrogen atoms with one hydrogen removed

biological group
  • Specialized
1 3.4

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

A Libyan armed group formed in 1995 that opposed the government and was linked to al-Qaeda

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.