abelian group Antonyms
No Synonyms and anytonyms found
Meaning of abelian group
Wordnet
abelian group (n)
a group that satisfies the commutative law
abelian group Sentence Examples
- An abelian group is a mathematical structure where the group operation is commutative, meaning the order of the elements doesn't affect the result.
- The integers under addition form a classic example of an abelian group.
- In abstract algebra, the study of abelian groups is essential for understanding algebraic structures with commutative properties.
- A fundamental theorem in the theory of finitely generated abelian groups states that every such group is isomorphic to a direct sum of cyclic groups.
- The concept of an abelian group is a generalization of the properties observed in addition of integers.
- Mathematicians explore the classification of abelian groups and their various structural properties.
- Abelian groups play a significant role in the study of algebraic structures and their applications in diverse mathematical fields.
- The direct product of two abelian groups is itself an abelian group, illustrating the closure under this operation.
- Group theory provides a comprehensive framework for analyzing and categorizing abelian and non-abelian groups.
- The study of abelian groups is foundational in algebraic structures, serving as a cornerstone in many mathematical disciplines.
FAQs About the word abelian group
a group that satisfies the commutative law
No synonyms found.
No antonyms found.
An abelian group is a mathematical structure where the group operation is commutative, meaning the order of the elements doesn't affect the result.
The integers under addition form a classic example of an abelian group.
In abstract algebra, the study of abelian groups is essential for understanding algebraic structures with commutative properties.
A fundamental theorem in the theory of finitely generated abelian groups states that every such group is isomorphic to a direct sum of cyclic groups.
