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Mathematical Group (Noun)

Meaning

A set that is closed, associative, has an identity element and every element has an inverse.

Classification

Nouns denoting cognitive processes and contents.

Examples

  • The concept of a mathematical group is fundamental in abstract algebra, as it forms the basis for many other algebraic structures.
  • The integers under addition form a mathematical group, as the sum of any two integers is an integer, and each integer has an additive inverse.
  • A mathematical group is often represented using the Cayley table, a square table that describes the binary operation of the group.
  • In calculus, the set of invertible matrices under matrix multiplication is a mathematical group, which is essential for solving systems of linear differential equations.
  • The set of rotations in three-dimensional space forms a mathematical group, as the composition of any two rotations is a rotation, and each rotation has an inverse rotation.

Synonyms

  • Group

Hypernyms

  • Set

Hyponyms

  • Subgroup
  • Abelian Group
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