Which one of the following is not necessarily a property of a group?
2018
Which one of the following is not necessarily a property of a group?
Answer: A. Commutativity — A group is defined as a set equipped with a binary operation satisfying specific axioms. The four necessary axioms are closure, associativity, existence of an…
- A.
Commutativity
- B.
Associativity
- C.
Existence of inverse for every element
- D.
Existence of identity
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Correct answer: A
A group is defined as a set equipped with a binary operation satisfying specific axioms.
The four necessary axioms are closure, associativity, existence of an identity element, and existence of inverses.
Commutativity is not included in the standard definition of a group.
Groups where the operation is commutative are specifically called Abelian groups.
Therefore, commutativity is not necessarily a property of all groups.