discrete mathematics , group theory

Question

Is commutative property sufficient for a group to be abelian?

Answer 1

Yes, commutative property is sufficient for a group to be Abelian. In fact, that's exactly is the definition of an Abelian Group.

Comments

@shraddha priya so abelian group need not be closed or associative or identity or inverse ?

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No, these 4 properties should be there of course. Abelin Group is a group which is commutative. Therefore all the properties of a group are also present in Abelian group obviously.

Answer 2

for a group to be abelian following properties must be satisfied

(1)closure

(2)associ.

(3)identity

(4)inverse

(5)commu.