Group and Field
Explore the abstract algebra objects group, abelian group, and field with examples.
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Group
A group G, over a binary operation, , and two elements , is defined with the following four axioms:
- Closure: A group is closed under , that is, the result of the operation is also a member of that group.
- Associativity: The result of a binary operation on three or more elements remains the same, regardless of the arrangement of parentheses.
- Identity: There exists an identity element, , under operation, such that operation between any element of the group, , and results in