Which of the following property/ies a Group G must hold, in order to be an…

Answer: The group must satisfy the commutative property only.

Reasoning:

• Group axioms: A group must satisfy closure, associativity, identity, and inverses.

• Abelian (commutative) additional requirement: The group operation must be commutative: for all a, b in G, a·b = b·a.

Notes on the other listed properties:

• The distributive property is not part of the definition of a group; it applies to algebraic structures with two operations (for example, rings), so it is irrelevant to deciding whether a group is Abelian.

• The term "symmetric property" is not a standard requirement in group definitions. Groups require inverses (each element has an inverse), but there is no separate "symmetric" requirement needed for an Abelian group.

Therefore, the only additional property needed for a group to be Abelian is commutativity.