commutative group (Meaning)
Wordnet
commutative group (n)
a group that satisfies the commutative law
Synonyms & Antonyms of commutative group
No Synonyms and anytonyms found
commutative group Sentence Examples
- A commutative group, also known as an abelian group, is a mathematical structure where the group operation is commutative.
- The integers under addition form a commutative group since the sum of any two integers is always the same, regardless of the order.
- The set of real numbers excluding zero under multiplication is a commutative group.
- The commutative property of addition and multiplication ensures that the real numbers form a commutative group.
- The group of rational numbers under addition is a commutative group, as the sum of any two rational numbers is commutative.
- The commutative property of the group operation allows for the interchangeability of elements in a commutative group.
- The symmetry of the group operation in a commutative group simplifies many mathematical calculations and proofs.
- In abstract algebra, the study of commutative groups is essential for understanding algebraic structures and their properties.
- The concept of a commutative group extends to other mathematical structures, such as rings and fields.
- The classification of finite abelian groups is a significant area of study within commutative group theory.
FAQs About the word commutative group
a group that satisfies the commutative law
No synonyms found.
No antonyms found.
A commutative group, also known as an abelian group, is a mathematical structure where the group operation is commutative.
The integers under addition form a commutative group since the sum of any two integers is always the same, regardless of the order.
The set of real numbers excluding zero under multiplication is a commutative group.
The commutative property of addition and multiplication ensures that the real numbers form a commutative group.
