write conditions for the groups and Abelian groups .
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Answer:
An abelian group is a nonempty set A with a binary operation + defined on A such that the following conditions hold: (i) (Associativity ) for all a, b, c ∈ A, we have a + (b + c)=(a + b) + c; (ii) (Commutativity ) for all a, b ∈ A, we have a + b = b + a; (iii) (Existence of an additive identity ) there exists an ...
Answer:
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.[1]
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