Definitions for commutative group
com·mu·ta·tive group

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Abelian group, commutative groupnoun

   a group that satisfies the commutative law

WikipediaRate this definition:0.0 / 0 votes

1. commutative group

   In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.

ChatGPTRate this definition:0.0 / 0 votes

1. commutative group

   A commutative group, also known as an abelian group, is a set equipped with an operation satisfying four fundamental conditions: 1. Closure: If 'a' and 'b' are in the group, then 'a * b' is also in the group. 2. Associativity: For all 'a', 'b', and 'c' in the group, (a * b) * c equals a * (b * c). 3. Existence of identity element: There is an element 'e' in the group such that for every element 'a' in the group, the equations 'e * a' and 'a * e' both return 'a'. 4. Existence of inverse element: For each element 'a' in the group, there exists an element 'b' in the group such that 'a * b' and 'b * a' both equal the identity element 'e'. In addition to these, a commutative or abelian group also follows the Commutative Law, which states that the result of performing the operation on any two elements in the set does not depend on their order, i.e. 'a * b' equals 'b * a'. An example of an abelian group is the set of integers with the operation being addition, because it satisfies all these properties.

Matched Categories

1. • Group

How to pronounce commutative group?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say commutative group in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of commutative group in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of commutative group in Pythagorean Numerology is: 3

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=commutative group
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Commutative_Group
3. ^ ChatGPT
   https://chat.openai.com