mathematical group
- noun
- /ˌmæθəˈmætɪkəl ɡruːp/
- Specialized
:
grupo matemático
- The concept of a mathematical group is fundamental in abstract algebra.
Examples
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Learning about the properties of a mathematical group helps in understanding advanced topics in mathematics.
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A mathematical group consists of a set and an operation.
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Symmetry operations in a crystal can often be described using a mathematical group.
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In abstract algebra, a mathematical group is fundamental.
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In abstract algebra, a mathematical group is defined by its elements and a binary operation that satisfies closure and associativity.
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The set of integers under addition forms a mathematical group because it includes an identity and inverses for every element.
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To understand symmetry, one must study how a mathematical group can describe the transformations that leave an object unchanged.
Synonyms
50
8.6
In mathematics, a set of elements with a rule for combining them that has an identity and inverses
Surface Forms
Morphology
The phrase is compositionally regular — 'mathematical' simply specifies the domain of 'group', so a learner who knows both words can infer it refers to a kind of group used in mathematics. However, the technical algebraic properties that define a group (closure, associativity, identity, inverses) are specialized and not derivable from the basic senses of the constituents, so full meaning requires prior mathematical knowledge.
Etymology
Mathematical group comes from a simple image: a group of moves that work like a small team, where you can combine any two moves and still get a move in the team, there is a 'do-nothing' move, and every move has an 'opposite' that undoes it. So, thinking of these moves as a team explains why the phrase means 'a set of things with a way to combine them, a neutral action, and an opposite for every action'.